Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.

The equation to find the height of the mountain prior to construction, represented by the variable h, is

1.1h – 622.5 = 5,675

Solve an equation to find the height of the mountain prior to construction, represented by the variable h.



h =
feet

Check the picture below.

[tex]tan(x) =\cfrac{\stackrel{opposite}{10}}{\underset{adjacent}{4}}\implies tan(x)=\cfrac{5}{2}\implies x=tan^{-1}\left( \cfrac{5}{2} \right)\implies x\approx 68.20^o[/tex]

Make sure your calculator is in Degree mode.

The length of the third side of the triangle is 2x+13.

According to the question,

We have the following information:

A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

We know that perimeter of triangle is the sum of all three sides of triangle.

Let's take its third side to be y.

So, we have the following expression:

3x+2x-5+y = 7x+8

5x-5+y = 7x+8

Adding 5 on both the sides:

5x+y = 7x+8+5

5x+y = 7x+13

Subtracting 5x from both the sides:

y = 7x-5x+13

y = 2x+13

Hence, the correct option is B.

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Answer:

B. 2x+13

Step-by-step explanation:

I got it right on the test

Answer:

[tex]\boxed{\sf y=37^o}[/tex]

[tex]\boxed{\sf x=74^o}[/tex]

[tex]\boxed{\sf z=25^o}[/tex]

Step-by-step explanation:

Let's first solve for y:-

*Linear pairs are supplementary angles, meaning there sum should be 180° *

[tex]\sf 2y^o+106^o=180^o[/tex]

[tex]\sf 2y=180-106[/tex]

[tex]\sf \cfrac{2y}{2} =\cfrac{74}{2}[/tex]

[tex]\boxed{\sf y=37^o}[/tex]

*Consecutive angles are also supplementary angles = 180°*

[tex]\sf x=2y[/tex]

[tex]\sf x=2(37)[/tex]

[tex]\boxed{\sf x=74^o}[/tex]

By corresponding angles,

[tex]\sf 4z+6=106[/tex]

[tex]\sf 4z+6-6=106-6[/tex]

[tex]\sf \cfrac{4z}{4} =\cfrac{100}{4}[/tex]

[tex]\boxed{\sf z=25^o}[/tex]

_____________________

Hope this helps!

Have a good day!

If she sold the gold bracelet at $2012, the profit would be $1212

Let  original price of the gold bracelet be x

Mrs Tan wanted to make a profit of 52%

The selling price would be $1216

Selling price = x + 52% of x

1216 = x + (52/100)x

1216 = 152/100x

x = 1216(100/152)

x = 800

The original price is $800

The price at which she sells the gold bracelet is 2012

Profit = selling price - original price

= 2012 - 800

= 1212

Therefore, if she sold the gold bracelet at $2012, the profit would be $1212

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The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2

A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.

The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.

The known elements of the set A in the question are; 2, 6, and 4

The elements of the set A are known as the domain of the function.

The known element of the set B are 8, 0, and 2

The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)

To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4

Therefore;

n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2

The correct statement is therefore;

n can be any value except 1, 3, or 2

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The height of the block that has dimensions of 10 cm and 12 cm and a volume of 1,800 cubic centimeters is 15 cm

A rectangular prism is a figure that has six faces that are rectangles.

The dimensions of the rock are;

Width of the rock = 10 cm

Length of the rock = 12 cm

Volume displaced by the rock = 1,800 cubic centimeter

Height of the rock = Required

Let h represent the height of the rock, we get;

Volume of a rectangular prism, V = Length × Width × Height

Volume of the rock = 10 × 12 × h = 1,800

h = 1,800 ÷ (10 × 12) = 15

Where the volume of the rock is 1,800 cubic centimeter, the height of the rock is 15 centimeters

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Answer:

Step-by-step explanation:

d- down four then right three

Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

As given in the question,

Let 'p' represent the population in thousands of people.

Let x represents the number of years.

Population projected in 2005 = 450,000 people

                                                 = 450 ( in thousand people)

Population increases by 4000 people each year that is equal to 4 (in thousand of people)

Required equation to represent the population in x years ( in thousand of people ) is given by:

p = 4x + 450

Population in 2010 is equal to :

p = 4 ( 2010 - 2005) + 450

 = 4(5) + 450

= 20 + 450

= 470 ( in thousand of people)

= 470,000 people

Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

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The slope of the line is 3/2, Equation of the line in point-slope form ( y - 10) = 3/2 (x-2), and The equation of the line in slope-intercept form

y = (3/2) x - 13

Using the slope formula, calculate the slope. To find the y-intercept (b), use the slope and one of the points.

Once you know the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line's equation.

Therefore,

A line goes through the points (2,10) and (-2,4).

Slope = (y2-y1)/(x2 -x1)

= (4 - 10) / (-2 - 2)

= -6/-4 = 3/2

The equation of the line in point-slope form using the point (2,10)

Slope  = 3/2

equation of the line in point slope form :

(y - y1) = m (x -x1)

(y - 10) = 3/2 (x-2)

y = mx + c

Simplifying the above equation, then we get

2 = 3/2 × 10 + c

c = 2 - 15

c = -13

equation of the line is

y = (3/2)x - 13

2y = 3x - 26

the slope-intercept equation of the line

y = (3/2) x - 13

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The age of the mammal is 3567 years.

Change the given numbers' letters in the equation to match:

N ="NOekt"

N-amount following t years

If not, the initial sum

K=0.0001t, where t=the number of years

Change the given numbers' letters in the equation to match:

0.70 = 1 * e^-0.0001t

Consider the two sides' logarithms:

t = -0.1549 / (-0.0001 * 0.43429) log0.70 = loge-0.0001t -0.1549 = -0.0001t * 0.43429 t = 3566.74

The age is 3,567 years, rounded to the nearest year.

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer:40%

Step-by-step explanation: Take 16 divided by 40 and you get .04, which equals 40 percent. Another way to think about it is this way: if 40 miles is the total distance, every 4 miles is 10% of the total. So 16 has to be 40%.

The subtotal before the surcharge and the sales tax is $12.25   .

In the question ,

it is given that ,

the total amount paid for the taxi ride = $13.73

sales tax percent charged = 4%

amount of surcharge = $1 .

let the subtotal before the tax and surcharge be "x"

the amount paid by the customer can be represented by the equation ,

total amount = cost + 4% of cost + surcharge

Substituting the values from above , we get

13.73 = x + 4% of x  + 1

4% of x + x = 13.73 - 1

0.04x + x = 12.73

1.04x = 12.73

x = 12.73/1.04

x = 12.24038

x ≈ 12.25

Therefore , The subtotal before the surcharge and the sales tax is $12.25   .

The given question is incomplete , the complete question is

A taxi ride cost a customer a total of $13. 73, which included 4% , percent sales tax and then a $1dollar surcharge. What was the subtotal before the surcharge and sales tax ?

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Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex]  =216

What is outcome of an event?

Suppose an event is happening. The result of the event is called outcome of the event.

For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die

Number of outcomes of rolling a die first time = 6

Number of outcomes of rolling the die second time = 6

Number of outcomes in rolling a die third time = 6

Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]

                                                                                   = [tex]6^3[/tex]

                                                                                   = 216

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Answer:

Step-by-step explanation:

-2y = -x -1
2y = x+1
y = 1/2x+1/2

Answer:

31. (25 - 8) x 3 = 51

32.  9 + 4 x (5 - 3) = 17

Step-by-step explanation:

grouping symbols

31.) 25 - 8 x 3 = 51

(25 - 8) x 3 = 51

Do the parentheses first

17 * 3 = 51

51=51

32.) 9 + 4 x 5 - 3 = 17

9 + 4 x (5 - 3) = 17

Parentheses first

9 + 4 * 2 = 17

Multiply

9+8 = 17

Add

17=17

Answer:

k = 13

Hope this helps : )

Step-by-step explanation:

To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.

1. Divide 7 on both sides of the equal sign.

7k = 91

7 7

2. Answer.

The 7 cancels out so we are left with k = 13 since

91 ÷ 7 = 13

k = 13

3. Check.

Plug in the variable "k."

7(13) = 91

91 = 91 ✓

Answer:

Step-by-step explanation:

Ok:

1. First write as equation!

x/3=4.5

2. Isolate the variable on the left side. Remember if a variable or number goes over equal sign, it becomes opposite

x/3=4.5

x=4.5*3

x=13.5

3. Double Check as always!!

13.5/3= 4.5

TRUE

Answer: 13.5

Answer:

13.5 is the answer ..hopefully this helps

Answer:

16.2

Step-by-step explanation:

16.18034 to 1 decimal place = 16.2

If it 2 decimal place =16.18

According to the central limit theorem, given a population with mean μ and standard deviation σ, if a suitably large random sample (n ≥ 30) is drawn from the population with permutation, the distribution of the sample mean will be approximately normally distributed. Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Then the mean of the sample mean is given by

[tex]\mu_ {x} =\mu[/tex]

and the standard deviation of the sample mean is given by

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]

The standard deviation of the sample mean is inversely proportional to the sample size n

so if n increases, the standard deviation decreases and vice versa.

(a) Sample size increased from 64 to 196.

As mentioned above, the standard deviation decreases as the sample size increases.

Therefore, increasing the value of n from 64 to 196 reduces the standard deviation of the sample mean.

n = 64 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{64} } \\\\\sigma_{x} = 0.7[/tex]

n = 196 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{196} } \\\\\sigma_{x} = 0.4[/tex]

sample mean standard deviation decreased from 0.7 to 0.4 n was 64 When it increased to 196.

Therefore the variance is also decreases.

(b)

decreace the sample size, increase the standard deviation.

Therefore, as the value of n decreases from 784 to 49, the standard deviation of the sample mean increases.

Standard deviation of sample mean for n = 784:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{784} } \\\\\sigma_{x} = 0.2[/tex]

Standard deviation of sample mean for n = 49:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{49} } \\\\\sigma_{x} = 0.8[/tex]

Standard deviation of sample mean increased from 0.2 to 0.8 while, n increased from 784 Then 49 decreases.

Therefore, the variance is also increases.

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Answer:

Step-by-step explanation:

she will pay $80 in interest.

The unit rate of the number of cups of water per cup of lime juice are;

Jaylan;

Wanchen;

Unit rate indicates the rate of an item for a quantity of one of another item such that when the quantitative relationship is expressed as a ratio, the denominator will be one.

The content of limeade Jaylan makes are;

The ingredient of the limeade Wanchen makes are;

The unit rate of water (cups) per lime juice (cups) is therefore;

Jaylan; 34 cups of water for every 15 cups of lime juice

Therefore;

34/15 cups of water for 1 cup of lime juice

34/15 = 2.2[tex]\overline 6[/tex]

The unit rate of the drink Jaylen makes is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juice

Wanchen; 35 cups of water per 12 cups of lime juice

Therefore;

35/12 cups of water per cup of lime juice

35/12 = 2.91[tex]\overline{6}[/tex]

The unit rate is 2.91[tex]\overline 6[/tex] cups of water per cup of lime juice

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Using the percentage, the truck is 342 inches long. So the option C is correct.

In the given question we have to find the length of the truck.

As given that, a car is 180 inches long.

A truck is 90% longer than the car.

The length of the car is 180 inches.

Truck is longer than the cars is 90%.

So the length of the truck = 180+180*90%

The percentage represent in the ratio of 100.

So the length of the truck = 180+180*90/100

Simplifying

The length of the truck = 180+162

The length of the truck = 342

Hence, the truck is 342 inches long. So the option C is correct.

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Answer:

  (s, f) = (4.5, 2.25)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Writing these in general form, we have ...

  3s +2f -18 = 0

  2s +3f -15.75 = 0

Using the "cross-multiplication method" for solution, we find ...

  ∆1 = (3)(3) -(2)(2) = 5

  ∆2 = (2)(-15.75) -(3)(-18) = 22.5

  ∆3 = (-18)(2) -(-15.75)(3) = 11.25

  s = ∆2/∆1 = 22.5/5 = 4.5

  f = ∆3/∆1 = 11.25/5 = 2.25

The solution is (s, f) = (4.5, 2.25).

__

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The points scored by Mrs. Dellett  on her 9th attempt is 210.

Given, Mrs. Dellett took up archery as a hobby.

On her first attempt she scored 18 points.

then every attempt after that, she increased her score by 24 points.

first attempt = 18 points

after this her score increased to 24 points on every attempt.

second attempt = 18+24 = 42

third attempt = 42+24 = 66

fourth attempt = 66+24 = 90

fifth attempt = 90 + 24 = 114

sixth attempt = 114 + 24 = 138

seventh attempt = 138 + 24 = 162

eight attempt = 162 + 24 = 186

ninth attempt = 186 + 24 = 210

Hence the option D is correct.

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The equation to represent the cost is C =  8 + 1.50x + 0.75y.

To write an equation that represents the cost of a pizza.

An equation that represents the cost of a pizza will be

C = 9 + 1.75x + 0.50y

   Fixed cost = $9

   Cost of additional inch = 1.75x

   Cost of additional topping = 0.50y

Total cost (C) will then be:

= 9 + (1.75 × x) + (0.50 × y)

C = 9 + 1.75x + 0.50y

Hence the answer is, the equation to represent the cost is C =  8 + 1.50x + 0.75y.

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Answer: x = 12, y = 15

Step-by-step explanation: 12/15 reduces to 4/5 because 12 divided by 3 is 4 and 15 divided by 3 is 5. 12 + 3 is 15 so if you add 3 to the numerator, you get 15/15, which is equal to 1.

The probability that he gets four or fewer questions correct is 0.9984

Let p be probability of getting correct answer and q be probability of getting in correct answer.

Number of trails :  n = 6

Number of Successes : x = 4

By using binominal distribution ,

P(x≤4) = 1 - P(x>4)

= 1 - [P(x = 5) + P(x = 6)]

= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]

solving combination ,

= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]

= 1 - (24 + 1 / 625)

= 1 - 25 / 625

= 624/625 = 0.9984

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