Solve for .
4x4<8 AND 9x + 5 > 23

The given triangle is a right angled triangle having the follwoing sides;

Hypotenuse = x (longest side)

Opposite = 14 (side facing the given acute angle)

Theta = 15 degrees

Using the SOH trigonometry identity;

sin 15 = opposite/hypotenuse

sin15 = 14/x

x = 14/sin15

x = 14/0.2588

x = 54.09

x is approximately equal to 54.1. Option B is coorect

The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%

The percentage of adult females have pulse rates below 90 bpm - 89.97%

a)

X ~  N ( µ = 74 , σ = 12.5 )

P ( 49 < X < 86.5 )

Standardizing the  value

Z = ( X - µ ) / σ

Z = ( 49 - 74 ) / 12.5

Z = -2

Z = ( 86.5 - 74 ) / 12.5

Z = 1

P ( -2 < Z < 1 )

P ( 49 < X < 86.5 )  =  P ( Z < 1 ) - P ( Z < -2 )

P ( 49 < X < 86.5 )  = 0.8413 - 0.0228

P ( 49 < X < 86.5 )  = 0.8186  ≈  81.86%

b)

X ~ N ( µ = 74 , σ = 12.5 )

P ( X < 90 )

Standardizing the value

Z = ( X - µ  ) / σ

Z = ( 90 - 74 ) / 12.5

Z = 1.28

P (  ( X - µ ) / σ )  < ( 90 - 74 ) / 12.5 )

P ( X < 90 ) =  P ( Z < 1.28 )

P ( X < 90 ) = 0.8997  ≈  89.97%

The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).

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Answer:

1,081 gallons

Step-by-step explanation:

1,119 - 38 = 1,081

Answer:golden hour by JVKE

Step-by-step explanation:

Answer:

y=3x+14

Step-by-step explanation:

First find the point using slope point form.

y-y₁=m(x-x₁)

Put y value in for y₁, x value in for x₁ and slope in for m.

y-2=3(x+4)

Simplify

y-2=3x+12

Solve for y to get slope intercept form Y=mx+b

y=3x+14

Answer:

y = - 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1

y = - 2x - 1 ← equation of line

In these linear expressions one is equivalent which is  3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.

Alternatively pluging; we will see that none of the exponents can be greater than 1.

2x - 3(1.3x - 2.5) = 5.9x + 7.5

2x -3.9x + 7.5 = 5.9 + 7.5

-1.9x + 7.5 ≠  5.9 + 7.5

thus linear expression is not equivalent.

3- 2( - 2.6x + 2.1) = 5.2x - 1.2

3 + 5.2x -  4.2 = 5.2x - 1.2

5.2x - 1.2 = 5.2x - 1.2

thus, linear expression is equivalent.

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Answer:

Step-by-step explanation:

Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.

To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.

Now, total distance in race

8/18 + 16/18

= (8+16)/18

= 24/18

= 4/3

= [tex]1\frac{1}{3}[/tex] kilometers

Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

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Answer:

x=62

Step-by-step explanation:

X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.

-Hope this helps

Answer:

Mexico to the United States in 1947

Step-by-step explanation:

Answer:

y = [tex]\frac{3x -6}{5}[/tex]

Step-by-step explanation:

3x - 5y = 6 ( subtract 3x from both sides )

- 5y = - 3x + 6 ( multiply through by - 1 )

5y = 3x - 6 ( divide both sides by 5 )

y = [tex]\frac{3x-6}{5}[/tex]

Therefore let us input the values to find the volume of the cone

The answer should be A.

Answer:

15/8 for exact form

1.875 for decimal form

And

1 and 7/8 for mixed number form

hope this helps you!

(also already in the simplest form :)

Given:

Product of two numbers is 1.

The one number is 5/2.

Let the another number be x.

Answer: Option a) is correct. the other number is 2/5.

Answer:

x = 7 , ∠ A = 36°

Step-by-step explanation:

since ∠ ADB ≅ ∠ CBD ( alternate angles )

and ∠ ABD ≅ ∠ CDB ( alternate angles )

then ABCD is a parallelogram

the opposite angles of a parallelogram are congruent , so

∠ C = ∠ A , that is

8x - 20 = 3x + 15 ( subtract 3x from both sides )

5x - 20 = 15 ( add 20 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°

Answer: x = 7 and m∠A = 36

Step-by-step explanation:

Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB

This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C

⇒3x +15 = 8x - 20

⇒3x + 15 - 3x = 8x - 3x -20

⇒5x = 20 + 15

⇒x = 7

Now m∠A = (3X7) +15 = 36

Answer:

b= -1, -6

Step-by-step explanation:

divide by common factor

then use x=- b+- sqrt b^2-4ac/2a

separate the equations and solve them

The length of XY=19.894 cm when the angle XYZ=90° and angle YZX=61° and the length of hypotenuse=17.4 cm. Using the property of trigonometry, a=b.sinα/sinβ.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Here,

a=b.sinα/sinβ

=17.4·sin(90°)/sin(61°)

=19.89436 cm

≈19.9 cm

When the hypotenuse is 17.4 cm long and the angles XYZ and YZX are 90° and 61°, respectively, the length of XY is 19.894 cm. Using the trigonometric formula a=b.sinα/sinβ.

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Table A shows a proportional relationship

What is proportional relationship?

When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.

In the figure we are given 2 tables

We plot both the curve on the graph we get

Table A shows a linear relationship where are Table b Does not shows a proportional relationship

Hence Table A shows a proportional relationship

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Answer:

Step-by-step explanation:

Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

Concept; Probability

Step1: The total number of tokens is

let the probability of blue be P(B) and the probability of red be P(R)

The probability that the first is Blue is

The probability the second is white without replacement is

Hence the combined probability of Blue and Red is

Therefore the probability that the first is blue and the second is white is 4/15

The equation of the car can be given as and the price of the car after 8 years is $4445.

What is an exponential function?

A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.

We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.

Let the original price of the car be [tex]P_{0}[/tex]

After two years the price of the car is $11200

Mathematically it can be given as

[tex]11200= P_{0}e^{2x}[/tex]

After 6 years the price of the car is $6100

Mathematically it can be given as

[tex]6100=P_{0}e^{6x}[/tex]

Dividing both equations we get,

[tex]1.83=e^{-4x}[/tex]

Which can also be written as

[tex]e^{4x}=0.54[/tex]

on solving we get,

x=-0.154

Hence the rate at which price of the car is dropping is

[tex]P=P_{0}e^{-0.154t}[/tex]

No we have to find the original price of the car

To do so we substitute t=2 in the equation

we get

11200=[tex]P_0e^{-0.308}[/tex]

On solving we get,

15240=[tex]P_0[/tex]

Now we find the price of the car after 8 years

P=15240·[tex]e^{-1.232}[/tex]

On simplifying we get

P=$4445

Hence the price of the car after 8 years will be $4445

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Answer:

x = 15

Step-by-step explanation:

150+3x-15=180 because of same-side interior angles therorem.

Then, we solve the problem to get 15.

Hope this helped! :)

If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute

Referring to the attached picture, the two triangles in a cone are similar. Hence,

r/h = 48/24

or

r = 2h.

The volume of the liquid is given by:

V = 1/3 . πr²h

Substitute r = 2h,

V = 1/3 . π(2h)²h = 4/3 . πh³

Take the derivative with respect to t

dV/dt = 4/3 .  3πh² . dh/dt

dV/dt = 4 .  πh² . dh/dt

Substitute dV/dt = -40 and h = 10

-40 = 4 .  π(10)² . dh/dt

dh/dt = - 0.0318 in./minute

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The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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Answer:

Step-by-step explanation:

she would have to use 3/4 of the ingrediants to the 400g of minced beef.

tomato sauce would be 600g

stock would be 225g

and red wine would be 225g

The quantity of chopped tomatoes is 600 g, of stock is 225 ml, and of red wine is 225 ml if Julie only has 300 g of minced beef.

The ratio is the comparison of two quantities to determine how frequently one quantity obtains the other. It can be shown as a fraction between two numbers.

Quantity of minced beef = 400 g

Quantity of chopped tomatoes = 800 g

Quantity of stock = 300 ml

Quantity of  red wine = 300 ml

Taking ratios of all the quantities, we get:

minced beef: chopped tomatoes:stock: red wine

= 400:800:300:300

= 100:200:75:75 ( Dividing by 4, as a common factor)

Multiplying the above ratio by three to make the quantity of minced beef 300 g

= 300:600:225:225

Thus, the quantity of chopped tomatoes is 600 g, the quantity of stock is 225 ml, and the quantity of red wine is 225 ml if Julie only has 300 g of minced beef.

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Answer:0.0008994

Step-by-step explanation:

Since the translation is 8 units right and 4 units down, we have to add 8 to the x coordinate and subtract 4 to the y coordinate.

R=(-2,1)

R' = (-2+8,1-4)= (6,-3)

R' = (6,-3)

Answer: 50%

Step-by-step explanation:

The error percent of the fish tank is 50%

Error percent:

Error percent means the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. It is also known as the percent error is the relative error multiplied by 100.

The formula to calculate the error percent is

δ = |vA - vE|/vA x 100

δ  = percent error

vA = actual value observed

vE = expected value

Given,

Raul estimated that a fish tank contained 20 gallons of water. He later  found that the fish tank had a 40-gallon capacity.

Here we need to calculate the error percent.

According to the error percent formula,

In this question

The estimated value = 20 gallons

Actual value = 40 gallons.

Now, we have to apply the values on the formula, then we get,

P% = (40 - 20)/40 x 100

P% = 20/40  x 100

P% = 1/2 x 100

P% = 0.5 x 100

P% = 50.

Therefore, the error percent is 50%.

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