How high is a tree that cast a 26ft shadow at the same time a6ft post casts a shadow which is 11ft long

Answer:

a

   The  90%  confidence interval is  [tex]52561.13 < \mu < 57540.8[/tex]

b

Confidence interval for the population men between $52561.13  up to $57540.8

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 25[/tex]

     The  sample mean is  [tex]\= x = \$ 55,051[/tex]

     The standard deviation is  [tex]\sigma = \$ 7,568[/tex]

Given that the confidence level is  90% then the level of confidence is mathematically represented as

             [tex]\alpha = 100 -90[/tex]

              [tex]\alpha = 10\%[/tex]

             [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the values is  

               [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically  represented as

               [tex]E = Z_{\frac{ \alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]E = 1.645 * \frac{ 7568}{ \sqrt{ 25} }[/tex]

             [tex]E = 2489.9[/tex]

The 90% confidence interval is mathematically evaluated as

       [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

     [tex]55051 - 2489.8 < \mu < 55051 + 2489.8[/tex]

     [tex]52561.13 < \mu < 57540.8[/tex]

Answer:

The answer is 4 + 4 + 4 - 4 = 8

Step-by-step explanation:

The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.

There are many complicated problems in this book made with the intention of using logic to find a value.

The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.

[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]

Let the smaller angle be x

Then, Larger angle would be x + 4°

❍ They are complementary angles.

So,

➙ x + x + 4° = 90°

➙ 2x + 4° = 90°

➙ 2x = 86°

➙ x = 86°/2 = 43°

Then, x + 4° = 47°

So, Our required answer:

❍ They are supplementary angles.

So,

➙ x + x + 4° = 180°

➙ 2x + 4° = 180°

➙ 2x = 176°

➙ x = 176°/2 = 88°

Then, x + 4° = 92°

So, Our required answer:

✌️ Hence, solved !!

━━━━━━━━━━━━━━━━━━━━

Answer:

its the 1st one

Step-by-step explanation:

they need to know what the Total

Answer:

English; 12

French; 9

Both; 7

Step-by-step explanation:

28 - 19 = 9, therefore there are only 9 students who can only speak French

28 - 16 = 12, therefore there are only 12 students who can only speak English

12 + 9 = 21, then subtract 21 from the 28 total students

28 - 21 = 7, therefore there are only 7 students who can speak both

Answer:

x = 31

ROS  = 62

Step-by-step explanation:

QOR + ROS = 90 degrees as indicated by the box

28+ 2x = 90

Subtract 28 from each side

2x = 90 -28

2x = 62

Divide by 2

2x/2 = 62/2

x = 31

ROS = 2x = 2*31 = 62

Answer:

C. x= 31; mZROS = 62°

Step-by-step explanation:

90=28+2x

2x= 90-28

2x= 62

x= 62/2

x=31°

2(x)= 2× 31 = 62

I hope I helped you^_^

Answer:

Ok, the first step is to count all the possible selections that we have and the number of options in each selection:

1) Sandwich: 2 options, ham or turkey.

2) Soup, 2 options, tomato or vegetable.

3) Drink, 2 options, coffee or milk.

(i assume that the sandwich and the soup are separated selections)

Now, if the customer chooses at random, the probability that in one given selection he selects a given outcome is equal to the number of options that match the outcome divided by the total number of options for that selection.

Then in the soup selection we have: options that match the outcome (one, is the vegetable soup). Total number of options = 2.

Then the probability is:

P = 1/2 = 0.5

or 0.5*100% = 50% in percentage form.

Answer:

1/2

Step-by-step explanation:

Answer:

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Step-by-step explanation:

Given:

Weight of patient = 110 lb

Dosage = 25 mg/kg/day

Find:

Total amount receive each day

Computation:

Weight of patient = 110 lb

1 lb = 0.453592

Weight of patient = 110 (0.453592)

Weight of patient = 49.89

Weight of patient = 50 kg (Approx)

Total amount receive each day = 50 kg × 25 mg/kg/day

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school [tex]n_1[/tex] = 42

sample size for the second school [tex]n_2[/tex]  = 34

so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.

the proportion of students with ear infection Is as follows:

[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095

[tex]\hat p_2 = \dfrac{18}{34}[/tex]  =  0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]

[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]

[tex]\bar p = \dfrac{34}{76}[/tex]

[tex]\bar p = 0.447368[/tex]

[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]

The pooled standard error can be computed by using the formula:

[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]

[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]

[tex]S.E = \sqrt{ 0.01177284105}[/tex]

[tex]S.E = 0.1085[/tex]

The test statistics is ;

[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]

[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]

[tex]z = \dfrac{-0.14845}{0.1085}[/tex]

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

Answer:

1st option, y = 5

Step-by-step explanation:

when the line is horizontal, it's parallel to the x axis

Answer:

y = 5

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through

The line passes through (- 7, 5 ) with y- coordinate 5 , then

y = 5 ← is the equation of the line

Answer:

15 parts must be shaded

Step-by-step explanation:

3/5 × 25 = 15

15/25 = 3/5

Have a great day.

15 parts must be shaded in order to cover three fifths of the rectangle.

"A rectangle has two pairs of equal opposite parallel sides, four right angles and two diagonals. The diagonals of a rectangle are congruent.

They also bisect each other. Each diagonal divides the rectangle into two congruent right triangles."

Given

A rectangle is divided into 25 equal parts.

Number of parts must be shaded in order to cover three fifths of the rectangle

= [tex]\frac{3}{5}[/tex] × [tex]25[/tex]

= 15

Checking whether the 15 parts must be shaded in order to cover three fifths of the rectangle

= [tex]\frac{15}{25}[/tex]

= [tex]\frac{3}{5}[/tex]

Hence, 15 parts must be shaded in order to cover three fifths of the rectangle.

Learn more about rectangle here

https://brainly.com/question/12019874

#SPJ2

Answer:

-1 <x < 7

(-1,7)

Step-by-step explanation:

open circle on the left means the number is greater than

-1 <x

Open circle on the right means the number is less than

x < 7

Since both statements are true. we combine them

-1 <x < 7

open circles means parentheses, closed circles mean brackets

Answer:

67 marbles

Step-by-step explanation:

15+30=45

45+22=67

Step-by-step explanation:

you cannot add some simple numbers ? you don't know how to use a calculator ?

to solve this yourself is way shorter than putting this in here.

15 + 22 + 30 = 67

Answer:

Step-by-step explanation:

Equation of a circle is given by

x² + y² + 2gx + 2fy + c = 0

To find the radius of the circle we use the formula

[tex]r = \sqrt{ {g}^{2} + {f}^{2} - c } [/tex]

where g and f is the center of the circle

From the question

x² + y² - 10x - 16y + 53 = 0

Comparing with the general equation above we have

2g = - 10 2f = - 16

g = - 5 f = - 8

c = 53

Substitute the values into the above formula

That's

[tex]r = \sqrt{ ({ - 10})^{2} + ( { - 8})^{2} - 53 } [/tex]

[tex]r = \sqrt{100 + 64 - 53} [/tex]

[tex]r = \sqrt{111} [/tex]

We have the final answer as

Hope this helps you

(a) Let [tex]A(t)[/tex] denote the amount of sugar in the tank at time [tex]t[/tex]. The tank starts with only pure water, so [tex]\boxed{A(0)=0}[/tex].

(b) Sugar flows in at a rate of

(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min

and flows out at a rate of

(A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min

so that the net rate of change of [tex]A(t)[/tex] is governed by the ODE,

[tex]\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}[/tex]

or

[tex]A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}[/tex]

Multiply both sides by the integrating factor [tex]e^{7t/1080}[/tex] to condense the left side into the derivative of a product:

[tex]e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

[tex]\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

Integrate both sides:

[tex]e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt[/tex]

[tex]e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C[/tex]

Solve for [tex]A(t)[/tex]:

[tex]A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}[/tex]

Given that [tex]A(0)=0[/tex], we find

[tex]0=\dfrac{378}5+C\implies C=-\dfrac{378}5[/tex]

so that the amount of sugar at any time [tex]t[/tex] is

[tex]\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}[/tex]

(c) As [tex]t\to\infty[/tex], the exponential term converges to 0 and we're left with

[tex]\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5[/tex]

or 75.6 kg of sugar.

Answer:

Step-by-step explanation:

The given piecewise function i

From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.

For x=-1,

LHL:  

Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.

For x=2,

LHL:  

Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.

Therefore, the correct option is A.

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

Step-by-step explanation:

angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer

Answer:

so angles in a triangle add up to 180,

32+50+m<MQP=180

82+m<MQP=180

m<MQP=180-82

=98°

and angles on a straight line add up to 180 therefore

m<MQR=180-m<MQP

=180-98

=82

I hope this helps and if you don't understand feel free to ask

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

Hi, there!!!

I hope you mean to evaluate cosA+ sonA /cosA - sinA.

so, i hope the answer in pictures will help you.

3x ⁴ = 3x ² • x ². Then

(3x ⁴ - 2x ³ + 4x - 5) - 3x ² (x ² + 4) = -2x ³ - 12x ² + 4x - 5

-2x ³ = -2x • x ². Then

(-2x ³ - 12x ² + 4x - 5) - (-2x) (x ² + 4) = -12x ² + 12x - 5

-12x ² = -12 • x ². Then

(-12x ² + 12x - 5) - (-12) (x ² + 4) = 12x + 43

So we've shown

[tex]\displaystyle \frac{3x^4-2x^3+4x-5}{x^2+4} = 3x^2 - \frac{2x^3+12x^2-4x+5}{x^2+4} \\\\ = 3x^2 - 2x - \frac{12x^2-12x+5}{x^2+4} \\\\ = \boxed{3x^2 - 2x - 7 + \frac{12x+43}{x^2+4}}[/tex]

Answer:

G.) 72°

Step-by-step explanation:

A regular pentagon has all it's sides equal.

And all it's internal angles = 108°

The sum of all it's internal angles= 540°

AEB = TRIANGLE

And sum of internal angles In a triangle= 180°

EBDC is quadrilateral and a quadrilateral has it's internal angles summed up to 360°

But DEB = CBE

Let DEB = X

x + x +108+108= 360

2x= 360-216

2x= 144

X= 144/2

X=72

DEB = 72°

Answer:

B is the correct answer.

Step-by-step explanation:

-2x+3y+z=-6

z=6

-2x+3y+6=-6

-2x+3y=-12

-2(3)+3(2)

-6+6=0 A is incorrect

-2(3)+3(-2)=-12

-6-6=-12

B is the correct answer.

I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.

Answer:

40 mL of 10% acid

80 mL of 25% acid

Step-by-step explanation:

x = volume of 10% acid solution

y = volume of 25% acid solution

Total volume is:

x + y = 120

Total amount of acid is:

0.10 x + 0.25 y = 0.20 (120)

Solve by substitution.

0.10 x + 0.25 (120 − x) = 0.20 (120)

0.10 x + 30 − 0.25 x = 24

0.15 x = 6

x = 40

y = 80

Answer:

330

Step-by-step explanation:

If d = distance, t = time, and s = speed, then the relationship between the 3 is s * t = d.

Solve for speed by dividing the distance over the time, s = d/t. Then, plug in the speed which in this case is 55 mph and then multiply by the time of 6 hours.

Answer:

$247

Step-by-step explanation:

$95 = 5 h

1 h = 95 ÷ 5 = $19/h

$19 × 13h = $247

she would make $247 after 13 hours of work.

Answer:

5 miles away

Step-by-step explanation:

If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.

This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.

We can use the Pythagorean theorem since this is a right triangle.

[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]

Hope this helped!

Answer:

5 miles away

Step-by-step explanation:

Answer:

It's 360

Step-by-step explanation:

2 x 180 = 360