A stained-glass window is shaped like a right triangle. The hypotenuse is 15feet. The length of one leg is three more than the other. Find the lengths of the legs.

Answer:

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

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer:

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as shown;

CI = xbar ± Z(б/√n)

xbar is the sample mean

Z is the value at 95% confidence interval

б is the standard deviation of the sample

n is the number of samples

Given xbar = 14.2, Z at 95% CI = 1.96, б = 0.70 and n = 9

Substituting this values into the formula;

CI = 14.2 ± 1.96(0.70/√9)

CI = 14.2 ± 1.96(0.70/3)

CI = 14.2 ± 1.96(0.2333)

CI = 14.2 ± 0.4573

CI = (14.2-0.4573, 14.2+0.4573)

CI = (13.7427, 14.6537)

Hence, the 95% confidence interval of the true mean is within the range

13.7≤[tex]\mu[/tex]≤14.7 (to 1 decimal place).

Answer:

9x9= 81

3x3x3x3=81

81 to the first power.

Step-by-step explanation:

I hope this helps in any way:)

Explanation:

f(x) and y are often used interchangeably. We are asked to find the x value(s) when y = 7.

Circle the rows where 7 shows up in the y column. You should find that x = -1 and x = 1 are circled as well.

So f(x) = 7 leads to x = -1 or x = 1. In other words, f(-1) = 7 and f(1) = 7 also.

For the function given the value of x can be two, one is 1 and the other one is -1 if the f(x)=7

A function relates an input to an output means it is a kind of relationship between the variable y and x. It is denoted through f(x).

A variable is defined as a quantity that may assume any one of a set of values.

How to find the value of x in a function?

In the question the function is given as:

Function is denoted through f(x) and f(x) shows the value of x. We know that the value of f(x)=7 which is given in the question. So we will take the value of x in the front of 7 which is written in the y column. We have got two values in this which are 1 and -1. So they both will be the values of x.

Hence the value of x for the function given in the question are -1 and 1

Learn more about functions at https://brainly.com/question/25638609

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Answer:

Option b = 90 degrees of freedom.

Step-by-step explanation:

So, in this particular Question we are given the following parameters or data or information which is going allow us to be able to solve this particular problem or Question;

=> "A regression analysis involved 8 independent variables"

=> "99 observations. "

Requirement : to determine the critical value of t for testing the significance of each of the independent variable's coefficient.

Hence, the formula below will used in Calculating or in the determination of the degree of freedom;

Degree of freedom= total number of observations - number of independent variables- 1.

Thus, slotting bin the values into the formula above, we have;

The degree of freedom = 99 - 8 - 1 = 90.

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Answer:

Step-by-step explanation:

Given,

As we know that the all sides of the square are equal.

Length of a square paper = 12 cm

Area of square = ?

Now, let's find the area of square

[tex] = {l}^{2} [/tex]

plugging the value of length,

[tex] {(12)}^{2} [/tex]

Evaluate the power

[tex] = 144[/tex] square cm

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

Given the half like of a material to be 8.3 hours and the amount of iron-52 left after t hours is modeled by the equation [tex]A(t) = A_0 a^{t}[/tex], we can get A(t) as shown;

At t = 8.3 hours, A(8.3) = 1/2

Initially at t = 0; A(0) = 1

Substituting this values into the function we will have;

[tex]\frac{1}{2} = 1 * a^{8.3}\\\\Taking \ the \ log \ of\ both \ sides;\\\\log(\frac{1}{2} ) = log(a^{8.3} )\\\\log(\frac{1}{2} ) = 8.3 log(a)\\\\\fr-0.30103 = 8.3 log(a)\\\Dividing\ both\ sides\ by \ 8.3\\\\\frac{-0.30103}{8.3} = log(a)\\\\log(a) = - 0.03627\\\\a =10^{-0.03627} \\\\a = 0.919878 (to\ 6dp)[/tex]

Answer:

Step-by-step explanation:

Given:      CS ≅ HR

           ∠CHS ≅ ∠HCR

           ∠CSH ≅ ∠HRC

Prove: CR ≅ HS

ΔCHS ≅ ΔHCR (Angle-Angle-Side, AAS, congruence property)

ΔICR ≅ ΔIHS (congruence property)

IS ≅ IR (similarity property)

CS ≅ HR (given)

Thus,

IC = IS + SC (addition property)

IH = IR + RH (addition property)

IC ≅ IH

Then,

CR ≅ HS (similarity property of triangles SCH and RHC)

Answer:

  see below

Step-by-step explanation:

The rotated location of D' is (-2, 1). The "arrow" points to the left. The attached figure is the best I could do with your distorted image.

You have to rotate the figure 90 counterclockwise about the origin.

75 meters

Step-by-step explanation:

5 x 30/2

= 5 x 15

= 75 meters

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Answer:

4

Step-by-step explanation:

Answer:

1/8 < 1/6

Step-by-step explanation:

The top is divided into 8 and 1 part is shaded so 1/8

The bottom is divided into 6 and 1 part is shaded so 1/6

Comparing

1/8 < 1/6

Answer:

20.25 miles

Step-by-step explanation:

If your car travels 27 miles on a full tank of gas, then your car will travel [tex]27\cdot\frac{3}{4}[/tex] miles on [tex]\frac{3}{4}[/tex] tank of gas.

[tex]27 \cdot 0.75 = 20.25[/tex]

I hope this helped!

Responder:

Explicación paso a paso:

Dado un polígono con los siguientes lados 3n + 5, n² - 4, n² - 4 y 3n + 5, el perímetro del polígono dado será equivalente a la suma de todos los lados del polígono. Como el polígono está formado por 4 lados, el perímetro de la forma será;

P = s₁ + s₂ + s₃ + s₄

P = (3n + 5) + (n² - 4) + (n² - 4) + (3n + 5)

P = 3n + 5 + n² - 4 + n² - 4 + 3n + 5

Recolectando los términos similares;

P = n² + n² + 3n + 3n + 5 + 5-4-4

P = 2n² + 6n + 10-8

P = 2n² + 6n + 2

Por lo tanto, el perímetro del polígono es 2n² + 6n + 2

*check attachment for the correct figure given in this question with the right labelled angles

Answer:

[tex] x = 86, y = 67, z = 94 [/tex]

Step-by-step explanation:

From the given figure attached below, values of x, y, and z can be found as follow:

Value of x:

[tex] x = 180 - (38 + 56) [/tex] => sum of angles in a triangle

[tex] x = 180 - 94 [/tex]

[tex]x = 86[/tex]

Value of z:

[tex] z = 180 - 86 [/tex] => angles on a straight line

[tex]z = 94[/tex]

Value of y:

[tex] y = 180 - (19 + 94) [/tex] => sum of angles in a triangle.

[tex] y = 180 - 113 [/tex]

[tex]y = 67[/tex]

[tex] x = 86, y = 67, z = 94 [/tex]

Answer:

.9375 days

Step-by-step explanation:

1.25 / 4 = 0.3125

0.3125 x 3 - 0.9375

Answer:

a. [tex]g(x)=f(x+3)+2[/tex]

b. [tex]g(x)=f(x-5)-4[/tex]

Step-by-step explanation:

Como f(x) no está especificada correctamente, vamos a tratarla genéricamente.

Las transformaciones que se proponen son traslaciones en el eje x y en el eje y.

Cuando se traslada'la función en el eje x, la variable independiente se reemplaza por una variable auxiliar u que es equivalente a la variable original x mas el valor desplazado hacia la izquierda.

Cuando se traslada la función en el eje y, simplemente se suma una constante a la función con un valor equivalente a las unidades que la función se traslado hacia arriba (si es hacia abajo, este valor es negativo).

Entonces, para trasladar f(x) 3 unidades a la izquierda u 2 unidades hacia arriba, empezamos por reemplazar la variable independiente por u=x+3 y luego agregar una constante igual a 2:

[tex]g(x)=f(x+3)+2[/tex]

Si queremos trasladar f(x) 5 unidades a la derecha y 4 unidades hacia abajo, empezamos por reemplazar la variable independiente por u=x-5 y luego agregar una constante igual a -4:

[tex]g(x)=f(x-5)-4[/tex]

En la figura se puede ver un ejemplo de la transformación para f(x)=x^2.

Answer:

Step-by-step explanation:

Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;

m = −0.05x²+3.5x−49

when m= 9

9 = −0.05x²+3.5x−49

−0.05x²+3.5x−49 = 9

0.05x²-3.5x+49 = -9

Multiplying through by 100

5x²+350x−4900 = 900

Dividing through by 5;

x²+70x−980 = 180

x²+70x−980 - 180 = 0

x²+70x−1160 = 0

Using the general formula to get x;

a = 1, b = 70, c = -1160

x = -70±√70²-4(1)(-1160)/2

x = -70±√4900+4640)/2

x = -70±(√4900+4640)/2

x = -70±√9540/2

x =  -70±97.7/2

x = -70+97.7/2

x = 27.7/2

x = 13.85mph

x ≈ 14 mph

Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph

Answer:

The hypothesis test is right-tailed

Step-by-step explanation:

To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.

While for a two tailed test, the claim always test for both options: greater and less than the mean value.

Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.

A test with the greater than option is right tailed while that with the less than option is left tailed.

Answer:

Please help with questions on my profile somebody

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.

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

y - 1 = 1/2x + 1

y = 1/2x + 2

Answer:

x ≥ 2 or x ≤ -6

Step-by-step explanation:

4|x + 2| ≥ 16

|x + 2| ≥ 4

x + 2 ≥ 4 or  -(x + 2) ≥ 4

x ≥ 2 or x + 2 ≤ -4 → x ≤ -6

[tex]\text{Solve the absolute value}\\\\4|x+2|\geq 16\\\\\text{We can make this equation a lot simpler by dividing both sides by 4}\\\\|x+2|\geq4\\\\\text{According to the absolute value, there can be two outcomes. In this case,}\\\text{it would be either:}\\\\x+2\geq4\,\,or\,\,x+2\leq-4\\\\\text{Solve first outcome:}\\\\x+2\geq4\\\\\text{Subtract both sides by 2}\\\\x\geq2\\\\\text{Solve second outcome:}\\\\x+2\leq-4\\\\\text{Subtract 2 from both sides}\\\\x\leq-6\\\\[/tex]

[tex]\boxed{x\geq2\,\,or\,\,x\leq-6}[/tex]

Answer:

Domain {1,2,3,4}

Step-by-step explanation:

The domain is the values for the input, in this case it is the x values

Domain {1,2,3,4}

Answer:

If you do not need that actual numbers, the answer is B.

Step-by-step explanation:

In order to find a fully comprehensive study, you would need many more people than just 10, not to mention these are the top 10 people in the world.

(Brainliest would be much appreciated!)

Answer:

[tex]g(2)=1[/tex]

Step-by-step explanation:

So first, we know that:

[tex]f(1)=g(1)+1[/tex]

And:

[tex]f(2)=2[/tex]

This means that instead of 1, if we put two in like so:

[tex]f(2)=g(2)+1[/tex]

Then we can substitute the f(2):

[tex]2=g(2)+1\\g(2)=1[/tex]

Therefore, g(2)=1.

Answer:

A. 6

Step-by-step explanation:

We see that 20 is a diameter that goes through the center of the point. This means that the top half of the black line is 10 and the top half of the blue line is 8. Use the Pythagorean Theorem to find out the length of the shortest side by doing 10^2 - 8^2 = x^2. x^2 = 36; x = 6.

Full Question

Of the cartons produced by a​ company, 10​% have a​ puncture, 6​% have a smashed​ corner, and 0.4​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing​ ____%. ​(Type an integer or a decimal. Do not​ round.)

Answer:

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Step-by-step explanation:

Given

[tex]Puncture\ Corner = 10\%[/tex]

[tex]Smashed\ Corner = 6\%[/tex]

[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]

Required

[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]

For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;

[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]

Substitute:

10% for P(Puncture Corner),

6% for P(Smashed Corner) and

0.4% for P(Punctured and Smashed Corner)

[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]

[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]

Convert % to fraction

[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]

Convert to decimal

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Using Venn probabilities, it is found that:

In this problem, the events are:

The "or" probability is given by:

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

Then:

[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]

The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.

To learn more about Venn probabilities, you can check https://brainly.com/question/25698611

Answer:

11 < √137 < 12

Step-by-step explanation:

the closest squares are 121 and 144; 11² and 12²

Answer:

16076.8

Step-by-step explanation:

Volume of Cylinder=πr²h

h= 20 m

r = 32/2 = 16

=πr²h

=  (3.14)(16^2)(20)

=16076.8 m^2

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!