Find the area of the triangle below. Be sure to include the correct unit in your answer.

Answer:

Step-by-step explanation:

the fourth option shows a list of the first 6 prime numbers

Answer: Option 4. 2, 3, 5, 7, 11, 13

Step-by-step explanation:

Remember, 1 is neither a prime number nor a composite number, it only has one factor.

So, we can exclude the first and second choice.

The third one has 9. But 9 is not a prime number.

Factor of 9: 1, 3, 9

It has 3 factors

So, this is not prime number and it should be excluded.

Hope this helps!! :)

Please let me know if you have any question

Answer:

It will take 7.5 gardeners to plant 45 trees in 45 minutes

Step-by-step explanation:

It takes 3 gardeners 30 minutes to plant 18 trees.

Let's determine the rate of this 3 gardeners

Rate= 18 trees/30 minutes

Rate= 2/5 trees per minute

So 3 gardeners= 2/5 trees per minute

But then one Gardner= 2/(3*5) trees per minute

One Gardner=2/15 trees per minute

Let's determine the number of gardeners it will take to plant 45 trees in 45 minutes

One Gardner=2/15 trees per minute

X(22 /3)= 2/15*(22.5/3)

It will take 7.5 gardeners to plant 45 trees in 45 minutes

Answer:

P = 1800

Step-by-step explanation:

The formula to calculate simple interest (I) is

I = [tex]\frac{PRT}{100}[/tex] ( note that time is in years ), thus

9 months = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75 years

Thus

81 = [tex]\frac{P(6)(0.75)}{100}[/tex] ( multiply both sides by 100 )

8100 = 4.5P ( divide both sides by 4.5 )

P = 1800

Answer:

0.2 repeating

Step-by-step explanation:

Answer:

27 and 60

Step-by-step explanation:

lets say the first number 'a' and the second number 'b'

1) The question says the sum of two number is 87 which means a + b = 87........given 1

2) we have another given which says one of the number is 6 morethan twice the other which means a = 2b + 6.......... given 2

a + b = 87

2b + 6 + b = 87 (we substitute 'a' with the given 2b + 6)

3b + 6 = 87

3b = 87 - 6

3b = 81

3b = 81

3 3

b = 27 ..... the first number

a = 2b + 6

a = 2 × 27 + 6

a = 54 + 6

a = 60..... the second number

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For any question comment me

Answer: 46

Step-by-step explanation:

Answer: z = 0 | Equation is not solvable

Step-by-step explanation:

We have 3 = 7 - 2(3z + 2)

When we distribute the 2, we get: -6z - 4 + 7 = 3

Combine like terms: -6z + 3 = 3

Subtract the left hand side 3 from the right hand side 3: -6z = 0

We can not divide by zero thus the equation is not solvable.

Answer:

Since BD bisects angle ABC, the resultant angles, angles ABD and CBD will be equal in magnitude. Since we are not given either the value of ABC nor are we given the figure, the answer we can get to from the given question is

angle ABD  = angle CBD

Answer: A

Step-by-step explanation:

To find the average rate of change, you use the formula [tex]\frac{f(b)-f(a)}{b-a}[/tex]. The best way to get the correct answer is to plug in each interval to make sure it equals 0.

-1 ≤ x ≤ 2: Correct

[tex]\frac{f(2)-f(-1)}{2-(-1)}[/tex]                                    [solve for f(2) and f(1)]

[tex]\frac{1-1}{3}=\frac{0}{3} =0[/tex]

------------------------------------------------------------------------------------------------------

-3 ≤ x ≤ -2: Incorrect

[tex]\frac{f(-2)-f(-3)}{-2-(-3)}[/tex]                                  [solve for f(-2) and f(-3)]

[tex]\frac{5-11}{1} =\frac{-6}{1}=-6[/tex]

------------------------------------------------------------------------------------------------------

-5 ≤ x ≤ 5: Incorrect

[tex]\frac{f(5)-f(-5)}{5-(-5)}[/tex]                                    [solve for f(5) and f(-5)]

[tex]\frac{19-29}{10} =\frac{-10}{10} =-1[/tex]

------------------------------------------------------------------------------------------------------

2 ≤ x ≤ 3: Incorrect

[tex]\frac{f(3)-f(2)}{3-2}[/tex]                                      [solve for f(3) and f(2)]

[tex]\frac{5-1}{1} =\frac{4}{1} =4[/tex]

------------------------------------------------------------------------------------------------------

After going through all the intervals, we found that A was the only one that has an average rate of change of 0.

Answer/Step-by-step explanation:

Maximum number of treats = amount of juice (58 in³) ÷ volume of cone-shaped container to be used

We are given different containers with the same height of 3 in, but different radius. Volume of a cone is given as ⅓*πr²h

Complete the table as follows:

Maximum no. of treats to be made with container of radius (r) 0.5 in, height 3 in:

Take π as 3.14

Volume = ⅓*3.14*0.5²*3 = 0.79 in³

Max no. of treats = 58 ÷ 0.79 = 73.4

73 containers can be filled completely. Therefore, maximum number of treats she could make is 73

Maximum no. of treats to be made with container of radius (r) 1 in, height 3 in:

Take π as 3.14

Volume = ⅓*3.14*1²*3 = 3.14 in³

Max no. of treats = 58 ÷ 3.14 = 18.5

18 containers can be filled completely, therefore, maximum number of treats to be made with this cone is 18 treats.

Maximum no. of treats to be made with container of radius (r) 1.5 in, height 3 in:

Take π as 3.14

Volume = ⅓*3.14*1.5²*3 = 7.07 in³

Max no. of treats = 58 ÷ 7.07 = 8.2

Max no of treats to be made is 8.

Answer:

G.

Step-by-step explanation:

cards = 2

dollars = 9

to check that the number of cards with the correct amount d;

use the ratio and proportion.

(3 x 18)/9 = 4

(4 x 31.5)/18 = 7

(7 x 45)/31.5 = 10

therefore, option G. table G. is the correct answer

try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount.  (see attached)

$4.27

(3.96) 1.08

4.27

Answer:

The median = Median = $77,153.5

Step-by-step explanation:

Given the data :

199999 98789 90878 87678 87245 83675 77876 77743 76564 76465 75643 66768 65654 58768 54678 51354

Measures of central tendency are used to describe the center or midpoint of a group of observation. They could include the mean, median and mode.

Mean described the average value of the distribution

Median, the middle observation.

Mode, the observation which occurs most

Using online calculator to save time ;

the mean = 83,111.06

Median = 77153.5

For the mode, all the values have a frequency of 1

Plotting the data on an histogram, it could be observed that the Data is positively skewed and hence, not symmetrical.

Since the distribution is not symmetrical, using the mean isn't the best and the mode is also not usable.

Therefore, the median seems to be the best of the 3 measures

Answer:

The 16th Century began on January 1st of 1600

Answer:

1 January 1501

hope it helps.

Answer: B) Shift 3 units down

Recall that y = f(x) as both describe outputs of a function. The same applies for g(x) as well. Saying f(x)-3 means y-3. So we're subtracting 3 from the y coordinate of each point. A point like (1,5) moves to (1,2). Doing this to all points on f(x) will move the entire curve down 3 units.

Answer:

347

Step-by-step explanation:

Answer:

Has not solution.

Step-by-step explanation:

14x÷2 = 6(x - 0)

14x÷2 = 6*x + 6*-0

14x÷2 = 6x - 0

14x = 2*6x

14x ≠ 12x

then:

This equation has not solution.

Answer:

$13.60 before sales tax

Step-by-step explanation:

$20 x .85 (aka 15% off) = $17

then

$17 x .80 (aka 20% off) = $13.60

Answer:

This is true

Step-by-step explanation:

Because a distribution of sample means is as the set of means from all the possible random samples of a specific size, selected from a specific given population.

===================================================

Work Shown:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)\\\\P(A \cap B) = 0.78 + 0.65 - 0.873\\\\P(A \cap B) = 0.557\\\\[/tex]

-------------

Side note:

A similar formula is [tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

We can isolate the last term to get the first equation shown above.

Answer:

===================================================

Work Shown:

-------------

Side note:

A similar formula is

We can isolate the last term to get the first equation shown above.

Step-by-step explanation:

Answer:

(0, 0.5)

Step-by-step explanation:

Let M is the midpoint of the line

x-coordinate of the midpoint:

xM = ( xA + xB ) / 2 = (-6 + 6) / 2 = 0

y-coordinate of the midpoint:

yM = (yA + yB) / 2 = (8 - 7) / 2 = 1/2 = 0.5

Answer: M (0, 0.5)

Answer:

(0, 0.5)

Step-by-step explanation:

Answer:

[tex]\huge\boxed{B. \ Perpendicular \ Lines}[/tex]

Step-by-step explanation:

The edges of length and width of a piece of printer paper perpendicularly intersect each other.

=> Perpendicular Lines are those making an angle of 90 degrees with each other.

Answer:

Perpendicular lines

Step-by-step explanation:

H.

Answer:

[tex]\Huge \boxed{\mathrm{14}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex](\frac{1}{4} )^{-2} - (5^0) (2)(1^{-1})[/tex]

Solving for exponents and multiplying:

[tex](4 )^{2} - (1) (2)(1)[/tex]

[tex]16-2[/tex]

Subtracting:

[tex]\Rightarrow \ 14[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]\huge\boxed{14}[/tex]

Step-by-step explanation:

[tex]\sf (\frac{1}{4} )^{-2} - (5^0 * 2 )* (1^{-1})[/tex]

Using law of exponents [tex]a^0 = 1[/tex] and [tex]1/a^m = a^{-m}[/tex]

=> [tex]4^2 - (1*2)*(1)[/tex]

=> [tex]16 - 2[/tex]

=> 14

Answer:

The correct option is (a).

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

In this case, a hypothesis test for a significant positive correlation is to be performed to determine whether the claim made by the policeman is true or not.

The hypothesis can be defined as follows:

H₀: There isn't a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ ≤ 0.

Hₐ: There is a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ > 0.

Consider the first option.

The sample correlation computed from 30 samples data is,

r = 0.38

The correlation is positive and the sample size is large enough to rely on the  sample data.

The p-value of the test is, p < 0.05.

As the p-value is less than 5% level of significance, the null hypothesis will be rejected.

Thus, concluding that there enough evidence to support the policeman's belief.

Thus, the correct option is (a).

3/196

Step-by-step explanation:

multiply everything

Answer: d.negatively skewed

Step-by-step explanation:

1

15

36

6

67

68

68

68

69

69

69

69

70

70

70

70

70

71

71

72

The distribution with the data above is negativey skewed. This was inferred from the histogram plot generated from the data.The output shows a distribution which has a long tail to the left and peaks to the right. This characteristics describes a distribution which is negatively skewed. Diagram of the obtained histogram for the distribution can be found in the attachment below.

Answer:

a.) 60

Step-by-step explanation:

Margin of Error formula = z × s/√n

z = z score of confidence interval

We are given z score of 99% = 2.58

s = Standard deviation = $36

Margin of Error= ± 12

n= unknown

= 12 = 2.58 × 36/√n

12 × √n = 92.88

√n = 92.88/12

√n = 7.74

Square both sides

(√n)² = 7.74²

n = 59.9076

Approximately n ≈ 60

Therefore, the required sample size = 60

Question options :

A)64

B)192

C)128

D)384

Answer:

B)192

Step-by-step explanation:

Please find attachment

Answer:

[tex]\Huge \boxed{9}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{3a}{b} -6= 21[/tex]

Add 6 to both sides.

[tex]\displaystyle \frac{3a}{b} =27[/tex]

Dividing both sides by 3.

[tex]\displaystyle \frac{a}{b} = 9[/tex]