A two story building measures 21 feet from the ground.A scale model shows the building to be 3 inches

Answer:

y=5x+5

Step-by-step explanation:

to find the slope of the line: 25-(-5)/4-(-2)=30/6=5

so the slope is 5

to find the y-intercept:

y=5x+b

25=5(4)+b (i used the point (4, 25) and plugged in 4 for x and 35 for y)

b=5

so, the equation of the line is: y=5x+5

Answer:

\(\frac{3}{10}\)

Step-by-step explanation:

\(\frac{45}{150}\)  15 can go into both 45 and 150 so you divide both into that

45/15 is 3

150/15=10

\(\frac{3}{10}\)

The value of x in the equation is 26.7

0.75x + 1.5y = 40

−1.5x − 1.5y = −60

add both equation to eliminate y .

Therefore,

−1.5x + 0.75x = -0.75x

1.5y + (- 1.5y) = 0

40 + (-60) = -20

Hence,

-0.75x  = - 20

divide both sides by -0.75

-0.75x / -0/75 = - 20 / -0.75

x = - 20 / -0.75

x = 26.6666666667

x = 26.7

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For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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Answer:

The sum of the numbers is 132

Step-by-step explanation:

First find the smallest number

Thus, you found the smallest number

then there sum given as 96+36=132

The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 1 3/8 pounds.

A line plot is a graphical representation of data that involves placing X's or other symbols above a number line to show the frequency of each value in a data set.

Each X represents one occurrence of the data value on the number line. Line plots are useful for quickly visualizing the distribution of a data set, especially when there are only a few unique values in the data set.

Based on the line plot, we can see that there are 2 dog toys that weigh 1/8 of a pound and 3 dog toys that weigh 3/8 of a pound.

To find the total weight of the dog toys that weigh 1/8 of a pound or 3/8 of a pound, we need to add the weights of these toys.

The total weight of the dog toys that weigh 1/8 of a pound is 2/8 of a pound, which simplifies to 1/4 of a pound.

The total weight of the dog toys that weigh 3/8 of a pound is 3 x 3/8 = 9/8 of a pound.

Adding these weights together, we get:

1/4 + 9/8 = 11/8 of a pound

This simplifies to 1 3/8 pounds.

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Answer: 1300

Step-by-step explanation:

3300-1000=2000

2000-450=1550

1550-150=1400

1400-100=1300

The true statements are C and E

the orange 2 correspond to the units, therefore, orange 2 = 2

the blue 2 correspond to the tens, therefore, blue orange = 20

now,

A is false because 20 isn't 200 times 2

b is false becuase 20 isn't 100 times 2

C is true because 2*10=20

D is false because they are indifferent posicitions, so they can't be equals

E is true because (1/10)*20=2

Answer: C, D

Step-by-step explanation:

\(x^2 +10x+18=0\\\\x=\frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2}\\\\x=\frac{-10 \pm \sqrt{28}}{2}\\\\x=-5 \pm \sqrt{7}\)

Answer:

\((g \cdot h)(x)=x^2-2x+23\)

Step-by-step explanation:

For composite functions, it's important to understand what the functions mean:

\((g\cdot h)(x)\)  which is read as "g of h, of x" means \(g ( \text{ }h(x) \text{ })\) which is read as "g of, h of x" (with slight pauses at the comma).  This means that x goes into the h function, and the output of the h function goes into the g function.

Putting "x" into the h function

\(h(x)=-x+4\)

Since it is just "x" going into the h function, the function as written is the output when x is the input.

Putting the h function output, into the g function

\(g(x)=x^2-6x+3\)

\(g(h(x))=(h(x))^2-6(h(x))+3\)

Substitute

\(g(h(x))=(-x+4)^2+-6(-x+4)+3\)

Squaring means the something multiplied by itself

\(g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3\)

Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):

\(g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3\)

Simplify the binomial terms:

\(g(h(x))=[x^2-8x+16]+[6x+4]+3\)

Group like terms:

\(g(h(x))=x^2-2x+23\)

Remember that \((g\cdot h)(x)\)  means \(g ( \text{ }h(x) \text{ })\)

\((g \cdot h)(x)=x^2-2x+23\)

So, \((g \cdot h)(x)=x^2-2x+23\)

Answer:

The  confidence interval is  \(0.304 < p < 0.324\)

Step-by-step explanation:

From the question we are told

      The sample proportion \(\r p = 0.314\)

      The margin of error  is \(E = 0.01\)

The confidence interval for  p is mathematically represented as

       \(\r p - E < p < \r p + E\)

=>    \(0.314 - 0.01 < p < 0.314 + 0.01\)

=>   \(0.304 < p < 0.324\)

The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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The value of \(\displaystyle\sf (-1+\sqrt{-3})^{33}+(-1-\sqrt{-3})^{33}\) is approximately -2.

Answer: 1:2

24 is half of 48

Step-by-step explanation:

b because you have to multiply

Answer:

Expanded Notation Form:

 91,360 =

 90,000  

+ 1,000  

+ 300  

+ 60  

+ 0  

Expanded Factors Form:

   91,360 =

 9 × 10,000  

+ 1 × 1,000  

+ 3 × 100  

+ 6 × 10  

+ 0 × 1  

Expanded Exponential Form:

 91,360 =

9 × 104

+ 1 × 103

+ 3 × 102

+ 6 × 101

+ 0 × 100

Word Form:

91,360 =

ninety-one thousand three hundred sixty

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Step-by-step explanation:

Answer:

PMT = $52,023.26

Step-by-step explanation:

To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:

PMT = PV x (r / (1 - (1 + r)^(-n)))

Where:

PMT is the periodic payment

PV is the present value (or desired future value) of the annuity

r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)

n is the total number of periods (in this case, 20 years)

We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))

PMT = $600,000 x (0.06 / (1 - 0.312))

PMT = $600,000 x (0.06 / 0.688)

PMT = $52,023.26

Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

Answer:

The 99% confidence interval is (-20.774, 2.774)

Step-by-step explanation:

The 60 seconds and 120 seconds breaking strength measures are;

60 seconds:  43, 52, 52, 58, 49, 52, 41, 52, 56, 51

120 seconds: 59, 55, 59, 66, 62, 55, 57, 66, 66, 51

The Mean and standard deviation for the data are obtained as follows;

The mean strength for the 60 seconds treatment samples, μX = 50.6 N

The standard deviation for the 60 seconds treatment samples, sX = 5.211099 N

The number of threads in the sample, n₁ = 10

The mean strength for the 60 seconds treatment samples, μY = 59.6 N

The standard deviation for the 60 seconds treatment samples, sY = 5.295701 N

The number of threads in the sample, n₂ = 10

The 99% confidence interval for the difference in mean, is given as follows;

\(\left (\mu X- \mu Y \right )\pm t_{\left(\dfrac{\alpha}{2}, df \right) } \cdot \sqrt{\dfrac{sX^{2}}{n_{1}}+\dfrac{sY^{2}}{n_{2}}}\)

The degrees of freedom, df = n₁ + n₂ - 2 = 20 - 2 = 18

(1 - α)·100 = 99%

α = 1 - 99/100 = 0.01

α/2 = 0.01/2 = 0.005

The critical-t at 0.005 significant level and df = 18 is 2.878

The confidence interval is therefore;

\(C.I. = \left (50.6- 59.6 \right )\pm 2.878 \right) } \times \sqrt{\dfrac{5.211099^{2}}{10}+\dfrac{5.295701^{2}}{10}}\)

C.I. = -9 ± 11.774425

∴ By rounding to three decimal places, the 99% confidence interval is (-20.774, 2.774).

The minimal surface area box has the following measurements: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(a) Let x be the side of the square base and y be the height of the box. Then the volume of the box is given by V = x²y = 125, and the surface area is given by S = 2x² + 4xy. We want to minimize S subject to the constraint that V is fixed at 125.

Using the volume equation, we can solve for y in terms of x: y = 125/x². Substituting this expression for y into the surface area equation, we get S(x) = 2x² + 4x(125/x²) = 2x² + 500/x.

To minimize S(x), we take the derivative with respect to x and set it equal to zero:

S'(x) = 4x - 500/x² = 0

Solving for x, we get x = 5√2/2. Substituting this value into the expression for y, we get y = 5√2.

Therefore, the dimensions of the box with minimal surface area are: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(b) Let x be the side of the square base and y be the height of the box. Then the surface area of the box is given by S = 2x² + 4xy = 44, and we want to maximize the volume V = x²y.

Using the surface area equation, we can solve for y in terms of x: y = (44 - 2x²)/4x. Substituting this expression for y into the volume equation, we get V(x) = x²(44 - 2x²)/4x = (11x² - x⁴/2).

To maximize V(x), we take the derivative with respect to x and set it equal to zero:

V'(x) = 22x - 2x³/2 = 0

Solving for x, we get x = √11. Substituting this value into the expression for y, we get y = (√11 - √2)²/2.

Therefore, the dimensions of the box with maximal volume are: side of base = √11, height = (√11 - √2)^²/2, and maximal volume = 11(√11 - √2)²/4.

(c) Using Newton's Method, we can approximate the root of f(x) = x³ - 12 starting with an initial guess of x₀ = 2:

x₁ = x₀ - f(x₀)/f'(x₀) = 2 - (2₃ - 12)/(32₂) = 1.833333

x₂ = x₁ - f(x₁)/f'(x₁) = 1.833333 - (1.833333³ - 12)/(31.833333²) = 2.005917

x₃ = x₂ - f(x₂)/f'(x₂) = 2.005917 - (2.005917³ - 12)/(3*2.005917²) = 2.000007

Therefore, the approximated root of f(x) = x³ - 12 using Newton's Method with an initial guess of 2 is x₃ = 2.000007.

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The equation to find how many miles Brooklyn ran is z = 1/3y.

Equation:

An equation is the statement of equality between two expressions consisting of variables and/or numbers.

Given,

Morgan, Nicholas, and Brooklyn had a challenge to see who could run the farthest in a week. Morgan ran 20 miles, Nicholas ran 14 times as many miles as Morgan and Brooklyn ran 1/3 as many miles as Nicholas.

Here we need to find the equation could you use to find how many miles Brooklyn ran.

Let x be the miles run by Morgan, y be the miles run by Nicholas and z be the miles rum by the Brooklyn.

So, it can be written as,

=> x = 20

=> y = 14x

=> z = 1/3y

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Answer:

x = -10

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

8x - 2(x + 1) = 7x + 8

Step 2: Distribute

8x - 2x - 2 = 7x + 8

Step 3: Combine like terms

6x - 2 = 7x + 8

Step 4: Subtract 6x on both sides

-2 = x + 8

Step 5: Subtract 8 on both sides

-10 = x

Step 6: Rewrite

x = -10

Answer:

\(\boxed{t=\frac{A-p}{pr}}\)

Step-by-step explanation:

\(A=p+prt\)

Subtract p on both sides.

\(A-p=p+prt-p\)

\(A-p=prt\)

Divide both sides by pr.

\(\displaystyle \frac{A-p}{pr} =\frac{prt}{pr}\)

\(\displaystyle{\frac{A-p}{pr} =t}\)

Answer:

A=p+prt

=>A/R=2pt

=>A/RT=2p

=>A/RTP=2

=>A/2RP=T

(1/4)(1x^2y + 32)

Substituting x = 8, y = 3, and z = 5/3:

(1/4)(1(8)^2(3) + 32) = (1/4)(192 + 32) = (1/4)(224) = 56

Therefore, the value of the expression is 56.

Answer: yes figure b is a scale copy of figure a

Step-by-step explanation:

figure A: 10, 10, 5 which can simplify to 2, 2, 1 while keeping the same ratio