Find the area of the triangle.
[?] square units

Answer:

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at  x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously =  x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank  .

Answer:

The numbers are 2 and 8.

Solution,

Let the numbers be X and 4x

[tex] \frac{1}{x} + \frac{1}{4x} = \frac{5}{8} \\ or \: \frac{1 \times 4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{5}{4x} = \frac{5}{8} \\ or \: 5 \times 4x = 5 \times 8(cross \: multiplication) \\ or \: 20x = 40 \\ or \: x = \frac{40}{20} \\ x = 2 \\ again \\ 4x \\ = 4 \times x \\ = 4 \times 2 \\ = 8[/tex]

hope this helps...

Good luck on your assignment..

Answer:

14

Step-by-step explanation:

630÷45=14

Answer:

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.

Answer:

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83

Step-by-step explanation:

Step(i):-

given mean of the population 'μ' = $19.67

Mean of the sample

                            [tex]= \frac{mean}{n} = \frac{19.67}{72} = 0.27[/tex]

Mean of the sample  μ₁ = 0.27

Step(ii):-

Given standard deviation of the  population  (σ) =  $7.02

Standard deviation of sample

                             [tex]= \frac{mean}{\sqrt{n} } = \frac{7.02}{\sqrt{72} } = 0.827[/tex]

Standard deviation of sample = 0.827≅ 0.83

Final answer:-

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83

Answer:

b) 0.0608

Step-by-step explanation:

As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed

Therefore the rain probability is

[tex]= \frac{T}{24}[/tex]

where,

T = Length of the time interval

Plus, as we know that rain is independent

So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes

i.e

= 5.91666 hours long.

So, P1 should be

[tex]= \frac{5.91666}{24}[/tex]

= 0.2465

Now we assume the probability of rain on day 2 is P2

So it would be same  i.e 0.2465

Since these events are independent

So, the total probability is

[tex]= 0.2465 \times 0.2465[/tex]

= 0.0608

Hence, the b option is correct

Answer: yes is it a function

Step-by-step explanation:

A graph is a function when there is only one y value for each x value. You can also use the vertical line test. This example is a “quadratic function”.

Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> [tex](2a)^2[/tex]

=> [tex](2^2*a^2)[/tex]

=> 4 * a²

=> 4a²

Answer:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex] = 1

Step-by-step explanation:

You have to calculate the following limit:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex]

To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}= \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1[/tex]

Hence, the limit is 1, L = 1

Answer:

30 different ways

Step-by-step explanation:

Hi

for the first topping she can choose 1 of 6 items

so she has 6 choices

and then the second topping she has 5 choices as each topping can only be chosen once

so it comes 6 * 5 = 30

Answer:

[tex]\dfrac{3x^2+34x+51}{2x^2+12x+18}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x+9}{2x+6}+\dfrac{8x+12}{x^2+6x+9}= \\\\\\\dfrac{3(x+3)}{2(x+3)}+\dfrac{8x+12}{(x+3)(x+3)}[/tex]

To add these two fractions, you need to make the denominators equal:

[tex]\dfrac{3(x+3)(x+3)}{2(x+3)(x+3)}+\dfrac{16x+24}{2(x+3)(x+3)}= \\\\\\\dfrac{(3x^2+18x+27)+(16x+24)}{2(x+3)(x+3)}= \\\\\\\dfrac{3x^2+34x+51}{2(x+3)(x+3)}= \\\\\\\dfrac{3x^2+34x+51}{2x^2+12x+18}[/tex]

Hope this helps!

Answer:

The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.

Step-by-step explanation:

We have a rectangular room with sides x and height y.

The volume of the room is 875 cubic feet, and can be expressed as:

[tex]V=x^2y=875[/tex]

With this equation we can define y in function of x as:

[tex]x^2y=875\\\\y=\dfrac{875}{x^2}[/tex]

The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:

[tex]A_w=xy=x\cdot \dfrac{875}{x^2}=\dfrac{875}{x}[/tex]

The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:

[tex]A_c=x^2[/tex]

We can express the total cost of painting as:

[tex]C=0.08\cdot (4\cdot A_w)+0.14\cdot A_c\\\\C=0.08\cdot (4\cdot \dfrac{875}{x})+0.14\cdot x^2\\\\\\C=\dfrac{280}{x}+0.14x^2[/tex]

To calculate the minimum cost, we derive this function C and equal to zero:

[tex]\dfrac{dC}{dx}=280(-1)\dfrac{1}{x^2}+0.14(2x)=0\\\\\\-\dfrac{280}{x^2}+0.28x=0\\\\\\0.28x=\dfrac{280}{x^2}\\\\\\x^3=\dfrac{280}{0.28}=1000\\\\\\x=\sqrt[3]{1000} =10[/tex]

The sides of the room have to be x=10 feet.

The height can be calculated as:

[tex]y=875/x^2=875/(10^2)=875/100=8.75[/tex]

The room will have sides of 10 feet and a height of 8.75 feet.

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]\frac{60}{4+1}[/tex]

[tex]\frac{60}{5} =12[/tex]

[tex]4:1[/tex]

[tex]4 \times 12: 1 \times 12[/tex]

[tex]48:12[/tex]

Answer:

Choice D.

Step-by-step explanation:

The number of points is obtained by the number of points of each multiple choice question times the number of multiple choice questions added to the number of points of each short answer question times the number of short answer questions.

Since the total number of points is 50, then the number of points from the multiple choice questions plus the number of points from the short answer questions add up to 50 points.

Answer: Choice D.

Answer:

D

Step-by-step explanation:

The number of points is 50, and short answer questions are 3 pts. Multiple choices are 1 pts.

So we have 3s+m=50

Answer:

  The discriminant is 0.

Step-by-step explanation:

The discriminant is zero if there is only one real solution to the quadratic equation.

__

A positive discriminant indicates 2 distinct real solutions; a negative discriminant indicates 2 distinct complex solutions.

Answer:

The Answer is C

Step-by-step explanation:

Answer: no, no, no, yes

Step-by-step explanation:

x=-3 is a vertical line. It goes straight up and down at x=-3. In order for the points to be on this line, the x-axis has to be -3. Looking at all the choices, all points are not a solution with the exception of (-3,0) which is right on the line.

Answer:

no no no yes

Step-by-step explanation:

i think

Answer:

126

Step-by-step explanation:

We multiply 42 × 3= 126

The measure of the angle is 126.

The measure of angle will be 66°.

What is Complementary angle?

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle.

Now,

Let the measure of angle = x

So, We can formulate;

⇒ (180 - x) = 42 + 3 (90 - x)

Solve for x as;

⇒ 180 - x = 42 + 270 - 3x

⇒ 180 - x + 3x = 312

⇒ 2x = 312 - 180

⇒ 2x = 132

⇒ x = 66

Thus, The measure of angle will be 66°.

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Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]

15 members:

This means that [tex]n = 15[/tex]

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

[tex]p = P(X = 0) + P(X = 15)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]

[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]

So

[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]

0.006% probability that the final vote count is unanimous.

Answer:

The height of the flagpole = 4.50m (3signifiant figures)

Question:

A tree and a flagpole are on the same

horizontal ground. A bird on top of the

tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.

Step-by-step explanation:

First we have to represent the above information with a diagram to enable us solve the question.

Then label them for easy identification.

To determine the distance between the tree and flagpole, we would apply tangent rule.

Let their distance = x

Tan60 = opposite/adjacent

Tan60 = 10.65/y

Tan60 × y = 10.65

y = 10.65/Tan60

y = 10.65/1.7321

y = 6.15m

See attachment for the concluding part

Answer:

  (a) b = (4/7)c

  (b) Bill: 40 shingles/hour; Chip: 70 shingles/hour

Step-by-step explanation:

Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...

  7b = 4c

  c - b = 30 . . . . shingles per hour difference in rates

(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7

  b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate

__

(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:

  7c -7b = 210

  7c -4c = 210

  c = 210/3 = 70

  b = (4/7)(70) = 40

Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.

Answer:

Third option.

Step-by-step explanation:

The triangles below are similar, because they have congruent corresponding angles.

Angle N is 105 degrees and angle Q is 105 degrees.

Answer:

im guessing thats on khan so 4=4  and 8 = 2:)

Step-by-step explanation:

Answer: Both

Step-by-step explanation: Both equal y intercept

Answer:

A. 12

Step-by-step explanation:

If we split an equalateral triangle down, it will become 2 30-60-90 triangles. Remember your 30-60-90 triangle rules.

6√3 = x√3, so x = 6

2(6) (for hypotenuse) = 12

Since the hypotenuse is one side of the bigger triangle, we have our final answer of 12.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

[tex] ME=0.03[/tex] the margin of error desired

[tex]Conf= 0.95[/tex] the level of confidence given

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

the critical value for 95% of confidence is [tex] z=1.96[/tex]

We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Answer:

Number of orders seen on last Tuesday = 605

Step-by-step explanation:

Number of orders seen on Tuesday = 600

It is given that it is 0.85% less than last Tuesday.

Let number of sales on last Tuesday = [tex]x[/tex]

As per question statement:

Number of order on last Tuesday - 0.85% of Number of order on last Tuesday = 600

OR

i.e. if we subtract 0.85% of x from x, it must be equal to 600.

[tex]x-\dfrac{0.85}{100}x =600\\\Rightarrow x-\dfrac{0.85}{100}x =600\\\Rightarrow \dfrac{100-0.85}{100}x =600\\\Rightarrow \dfrac{99.15}{100} \times x =600\\\Rightarrow x =\dfrac{600\times 100}{99.15}\\\Rightarrow x =\dfrac{60000}{99.15}\\\Rightarrow x \approx 605[/tex]

So, there were about 605 order seen last Tuesday.

Answer:

Step-by-step explanation:

Hello!

The Psychomotor Development Index (PDI) has an average value of μ= 100

The Mental Development Index (MDI) has an average value of μ= 100

At an approximate age of 1 year of normal healthy infants.

Using the group data set heart = 1 for all calculations (see attachment for complete table), you can define two variables of interest and obtain the descriptive statistics:

X₁: PDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₁= 69

X[bar]₁= 97.61

S₁= 14.73

X₂: MDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₂= 69

X[bar]₂= 106.33

S₂= 14.67

a)

You have to test the hypothesis that the average PDI for kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

H₀: μ₁ = 100

H₁: μ₁ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_1-Mu_1}{\frac{S_1}{\sqrt{n_1} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{97.61-100}{\frac{14.73}{\sqrt{69} } } = -1.347[/tex]

p-value: 0.17798

Using this approach the decision rule is:

The p-value is greater than the level of significance, the decision is to not reject the null hypothesis. Then the average PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

b)

H₀: μ₂ = 100

H₁: μ₂ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_2-Mu_2}{\frac{S_2}{\sqrt{n_2} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{106.33-100}{\frac{14.67}{\sqrt{69} } } = 3.584[/tex]

p-value: 0.000338

Using this approach the decision rule is:

The p-value is less than the level of significance, the decision is to reject the null hypothesis. Then the average MDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is different from 100.

c)

[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

95% CI for PDI

X[bar]₁ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_1}{\sqrt{n_1} }[/tex]

97.61 ± 1.96 * [tex]\frac{14.73}{\sqrt{69} }[/tex]

[94.134; 101.086]

95% CI for MDI

X[bar]₂ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_2}{\sqrt{n_2} }[/tex]

106.33 ± 1.96 * [tex]\frac{14.67}{\sqrt{69} }[/tex]

[102.869; 109.791]

The CI for the mean PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life contains 100, this is to be expected since the null hypothesis in the hypothesis test made at complementary confidence level, was not rejected.

I hope this helps!

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 162, \sigma = 8[/tex]

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{150 - 162}{8}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{180 - 162}{8}[/tex]

[tex]Z = 2.25[/tex]

[tex]Z = 2.25[/tex] has a pvalue of 0.9878

X = 160

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{160 - 162}{8}[/tex]

[tex]Z = -0.25[/tex]

[tex]Z = -0.25[/tex] has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

Answer:

Dear Yates

Answer to your query is provided below

Total Price for her vehicle will be $20600

Step-by-step explanation:

Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:

$22750 - $8000 = $14750.

Now, add the package upgrade ($5050) and the delivery charge ($800).

$14750 + $5050 + $800 = $20600.

The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The initial cost of the vehicle is = $ 22,750

Now , Edith has asked for an upgrade to a premium package for which the cost is $5050

So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800

Now , the delivery charge of the vehicle = $ 700

And , the updated total price = $ 27,800 + $ 700 = $ 28,500

Now , the dealer has offered her $8000

So , the final price of the vehicle = updated total price - $ 8000

On simplifying the equation , we get

The final price of the vehicle A = $ 28,500 - $ 8,000

The final price of the vehicle A = $ 20,500

Hence , the final price of the vehicle is $ 20,500

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Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

20% chance of striking oil.

This means that [tex]p = 0.2[/tex]

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]

Strike during the 7th drill, with 0.2 probability. So

[tex]P = 0.2P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]

Then

[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]

4.92% probability that the third strike comes on the seventh well drilled