3. A line with a slope of passes through the point (10,-5).
The equation of the line in slope intercept form
can be given by the formula y = mx + b
where m=
and b =
√x

The probability that at least 8 patients show improvement is; 0.94

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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Answer:

0

Step-by-step explanation:

8z +12 = 12

8z = 0

z =0

Answer:

The answer is 0

Step-by-step explanation:

4(2z+3)=12?=

We use the distributive property to distribute the 4 into the 2.

8z=3=12?=

8 + 3 is 12 so the z has no part to play in this.

z=0

You could also have divided from both sides of the equation, but doing it this way is easier for me.

Answer:

IM  and  YM

Step-by-step explanation:

not sure about the symbol part, but it's a ray !!

Answer: IM and YM

Step-by-step explanation:

It can be broken down into to different rays

From ratio concept, the greater number number is 32 .

A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)

Let the greater number be x .

The ratio given is 3:8 .

Thus, by the concept of ratio -

⇒ 3/8 = 12/x

⇒ x = (8/3 * 12)

∴  x = 32

Therefore, from ratio concept, the greater number number is 32 .

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Answer:

here ya go :)

the black line is y=-2x-3

the lavender line is y=-x+6

The difference between using Area and Volume with 2D and 3D figures is that Area is a measure of square units while Volume is a measure of cubic units.

The area of an object is the measure of space occupied by the two-dimensional object (flat) in a plane. Volume on the other hand is the quantity of space occupied by the object, 3-dimensional object in this case. The unit of area is in square units. The unit of volume is in cubic units.

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The median age of your customer base = 45

The median is the value that divides a data sample, a population, or even a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "typical" value because it is not skewed by the a small proportion of extremely large or small values. Due to the fact that income distribution can be highly skewed, the median income, for instance, might be a better indicator of what is considered a "typical" income.

Mean = middle term

          = 6th term

          = 45

Hence, Median of age = 45.

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Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

The value of the function at the point where the value of x is equal to zero is known as the y-intercept.

f(x)=-6(1.05)^x

Considering x

x=0

f(0)=-6(1.05)^0

f(0)=-6(1)

f(0)=-6

Therefore, the y-intercept is point (0,-6)

Generally, the equation for the function of the y-intercept of g(x) is  mathematically given as

From table

at x=0

The y-intercept is the point (0,-3)

Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

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The expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

From the question, we are to write an expression for each of the given statement

a. the sum of 6 and z

That is,

6 + z

b. the difference between 20 and x

That is,

20 - x

c. 8 less than the quotient of x divided by 6

That is,

x/6 - 8

d. x increased by 5 divided by 4

That is,

x + 5/4

Hence, the expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

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Answer: 12/4

Step-by-step explanation: whole number = 3. given denominator = 4. 4/4 = 1. 1 times 3 = 3. 4 plus 4 plus 4 = 12. therefore answer is 12/4

Answer:

87.5%

Step-by-step explanation:

Given:

Area of triangle NCM

⇒ 1/2 × base × height

⇒ 1/2 × CN × CM

⇒ 1/2 × 5 × 4

⇒ 10cm²

Length of rectangle ⇒ 10

Breadth of the rectangle ⇒ 8

↓

Area of rectangle ⇒ Length × Breadth

Area of rectangle ⇒ 10 × 8 = 80cm²

Area of shaded region ⇒ Area of rectangle  -  Area of triangle

Area of shaded region ⇒ 80 - 10 = 80cm²

Percentage of the shaded region = Shaded/complete rectangle × 100

⇒ 70/80 × 100 = 87.5

⇒ The percent of the area of the rectangle shaded is therefore 87.5%.

The blank space to form a linear pair with m∠BPD is m∠APD.

Linear pair of angles are formed when two lines intersect each other at a single point.

Linear pair angles are adjacent to each other.

Therefore, the sum of a linear pair angles is equals to 180 degrees.

This means linear pair angles are supplementary.

Hence,

m∠APD + m∠BPD = 180°

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Using the Empirical Rule and the Central Limit Theorem, we have that:

It states that, for a normally distributed random variable:

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, the standard deviation of the distribution of sample means is:

[tex]s = \frac{0.657}{\sqrt{50}} = 0.09[/tex]

68% of the means are within 1 standard deviation of the mean, hence the bounds are:

99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:

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Answer:

About 68% of the sample means fall within the interval $1.64 and $1.82.

About 99.7% of the sample means fall within the interval $1.45 and $2.01.

Step-by-step explanation:

To verify the given intervals, we need to calculate the standard error of the mean (SE) for a sample size of 50 using the population mean and standard deviation provided.

The standard error of the mean (SE) can be calculated as:

SE = population standard deviation / √(sample size)

Given that the population mean is $1.73 and the population standard deviation is $0.657, and the sample size is 50:

SE = $0.657 / √50 ≈ $0.09299 (rounded to 5 decimal places)

Now, we can calculate the intervals:

For the interval where about 68% of the sample means fall:

Interval = (Mean - 1 * SE, Mean + 1 * SE)

Interval = ($1.73 - $0.09299, $1.73 + $0.09299)

Interval ≈ ($1.63701, $1.82299)

So, about 68% of the sample means fall within the interval $1.64 and $1.82, which matches the given statement.

For the interval where about 99.7% of the sample means fall:

Interval = (Mean - 3 * SE, Mean + 3 * SE)

Interval = ($1.73 - 3 * $0.09299, $1.73 + 3 * $0.09299)

Interval ≈ ($1.54703, $1.91297)

So, about 99.7% of the sample means fall within the interval $1.55 and $1.91, which is different from the given statement.

The correct interval for about 99.7% of the sample means, rounded to the nearest hundredth, is $1.55 and $1.91, not $1.45 and $2.01 as mentioned in the statement.

Answer: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.

Step-by-step explanation:

Vertex of the equation is (-2, 5)

Focus of the equation is (-2, 8)

Directrix of the equation is 2

What is a Quadratic curve?

A quadratic curve is a parabolic curve is a graph of the points which define a quadratic function. It shows how a function behaves in the cartesian plane.

Quadratic curve may bend upwards, or downwards depending on the gradient of the curve.

Analysis:

setting the equation in the form, [tex]x^{2}[/tex] +4x -12y = -64 in the form [tex](x-h)^{2}[/tex] = 4p(y-k)

Firstly we take -12y to the right hand side

[tex]x^{2}[/tex] +4x = 12y - 64

Making the left hand side a perfect square expression, we square both sides with -2

[tex]x^{2}[/tex] +4x + [tex](2)^{2}[/tex] = 12y -64 + [tex](2)^{2}[/tex]

[tex](x+2)^{2}[/tex] = 12y -60

[tex](x+2)^{2}[/tex]  = 12(y - 5)

comparing with the other equation

-h = , h = -2, -k = - 5 k = 5, 4p = 12, p = 3

Vertex is (h, k) = (-2, 5)

Focus is (h, k+p) = (-2, 5+3) = (-2, 8)

Directrix is y = k-p = 5 - 3 = 2

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The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

According to the question

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9 :

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3 :

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

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hi

f°g  mean apply  g(x) and  then use result of  g(x) as  "x" in f(x)

so as  g(x) = x² +1   and  f(x) = 3x+2

so if we call  g(x)   X  we have  

f( X) =  3 X +2

now we replace  " X"  for it's value

f(X) =  3 ( x² +1) +2

f(X) =  3x² +3 +2

f(X) = 3x² +5

so  f°g = 3x² +5

Answer:

Give the opposite of each number : a. -3; b. 9; c. 5; d. -12

Solve each of the following problems : a. 3; b. 3; c. -18; d. 18; e. -6; f. -4

Solve each problem. Be sure to include the correct sign in your answer :

a. 24; b. -35; c. 54; d. -4; e. 8; f. -6

Answer:

Step-by-step explanation:

1.a. –3

b. 9

c. 5

d. –12

2. a. 9 + (–6) = 3

b. (–5) + 8 = 3

c. (–12) + (–6) = –18

d. 10 – (–8) = 18

e. (–4) – (+2) = –6

f. –9 – (–5) = –4

3. a. 8 × 3 = 24

b. –7 × 5 = –35

c. –6 × (–9) = 54

d. 8 ÷ (–2) = –4

e. –24 ÷ (–3) = 8

f. –36 ÷ 6 = –6

5. Multiply the service charge by the number of months in a year.

12 × 7 = $84

Answer: $84 is deducted per year.

6. Add the balance of each year to determine the closing balance.

–$1500 + (–$1200) = –$2700

penn foster

Answer:

6.2 pounds

Step-by-step explanation:

$5.58 / $.9 = 6.2 pounds of carrots bought

Answer: Answer C is correct, 50.9.

Assume that the entries have not been made. The effect that these errors have on the reported net income is: Net income will be overstated by $17,000.

Using this formula

Net income=Expired rent+Depreciation+Supplies

Let plug in the formula

Net income=$6400+$7600+$3000

Net income=$17,000 (Overstated)

Therefore the net income will be overstated by $17,000.

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By using excel sheet we can get the answers for the difference t test.

The two kinds of formula are used in the excel . One from the data analysis the t test assuming equal variances as nothing was mentioned.

But if the t test for the means is used there might be slight variation in the values.

The other formula was of descriptive statistics.

The data was

No of feedback (sec) Feedback (sec) Difference

45 54 9

33 50 17

59 58 -1

32 38 6

30 42 12

27 35 8

29 38 9

59 66 7

64 65 1

38 55 17

For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.

The null hypothesis is accepted because t stat= -1.322 is less than t critical which is  t critical= ±2.119  and lies in the acceptance region.

The p- value is 2.04 which is greater than alpha= 0.05

The t stat for 0.01=  4.561578674 and t Critical two-tail 3.249835541

The t stat is greater than t critical at alpha 0.01 so it is rejected.

The difference t test gives

Count=N   9                  9

Mean        41.2             49.67

Mean Difference  8.4

Standard Deviation  14.967       11.97

Variance        223.944  143.25

Standard Error 2.0824

t       = -1.322

df = 16

t Critical two-tail 2.119905285

Confidence Level(95.0%) 4.802039614

Lower CI (95.0%) =  3.6

Upper CI(95.0%)=  13.2

t stat for 0.01=  4.561578674

t Critical two-tail 3.249835541

Confidence Level(99.0%) 6.055710988

Lower CI (99.0%) =  2.345

Upper CI(99.0%)=  14.457

For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.

The null hypothesis is accepted because t stat= -1.322 is less than t critical which is  t critical= ±2.119  and lies in the acceptance region.

The p- value is 2.04 which is greater than alpha= 0.05

The t stat for 0.01=  4.561578674 and t Critical two-tail 3.249835541

The t stat is greater than t critical at alpha 0.01 so it is rejected.

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Answer:

Step-by-step explanation:

for horizontal line slope m=0

eq. of horizontal line at (0,7) with slope 0 is

y-7=0(x-0)

y-7=0

or

y=7

slope of vertical line=∝

eq of vertical line through (0,7) is

y-7=∝(x-0)

or

x-0=0(y-7)

x-0=0

or

x=0

The appropriate  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

Sheffield corporation entries

Debit Cash $18,870

[$21500-($480+ ($21500×10%))]

Debit Advertising expense $480

Debit Commission expense $2,150

(21,500×10%)

Credit Revenue from consignment sales $21,500

Debit Cost of goods sold $13,888

[($20400+$2000)×62%]

Credit Inventory on consignment $13,888

Therefore  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

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The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

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Answer: A

Step-by-step explanation:

[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]

The amount of money Craig paid more than Tim if the shop has an offer of reduction if a particular amount is spent is £88.

The shop discount:

£5 reduction if you spend more than £100

or

£10 reduction if you spend more than £140

or

£20 reduction if you spend more than £180

Cost of a shirt = £49

Tim buys 3 shirts

Total cost of Tim's shirt = £49 × 3

= £147

Amount Tim paid = £147 - £10

= £137

Craig buys 5 shirts

Total cost of Craig's shirt = £49 × 5

= £245

Amount Craig paid = £245 - £20

= £225

Difference between Tim and Craig's pay = £225 - £137

= £88

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The expression p% of m changed into an algebraic expression is pm/100

p% of m

= p% × m

= p/100 × m

= (p × m) / 100

= pm/100

Therefore, the expression p% of m changed into an algebraic expression is pm/100

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Using proportions, the expression for the final amount is:

150(1+d).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, we have that:

Hence the equivalent expression is:

120 x 1.25 x (1 + d) = 150(1+d).

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The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3

In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:

- 5 · p + q = - 25

- 3 · p + q = - 9

(p, q) = (8, 15)

The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:

y = x² + 8 · x + 15

y + 1 = x² + 8 · x + 16

y + 1 = (x + 4)²

(h, k) = (1, 4)

And lastly we must solve for x in the following inequality:

x² + 8 · x + 15 < x + 3

x² + 7 · x + 12 < 0

(x + 3) · (x + 4) < 0

- 4 < x < - 3

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