A right triangle has side lengths 7, 24, and 25 as shown below. Use these lengths to find cos B, tanB, and sin B.​

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Work Shown:

a^2+b^2 = c^2  ... pythagorean theorem

c = sqrt(a^2+b^2)

c = sqrt(4^2+12^2)

c = 12.6491106406736

c = 12.65

Answer:

Step-by-step explanation:

Given,

Height of the triangle = 4

Base of the triangle = 12

Therefore,

Hypotenuse of the triangle

[tex] {(base)}^{2} + {(height)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] = > {(12)}^{2} + {(4)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] = > {(hypotenuse)}^{2} = 144 + 16[/tex]

[tex] = > {(hypotenuse)}^{2} = 160[/tex]

[tex] = > hypotenuse = \sqrt{160} [/tex]

[tex] = > hupotenuse = \sqrt{5 \times 2 \times 2 \times 2 \times 2 \times 2} [/tex]

[tex] = > hypotenuse = 2 \times 2 \sqrt{5 \times 2} [/tex]

[tex] = > hypotenuse = 4 \sqrt{10} \: (ans)[/tex]

Answer:

23.42

Step-by-step explanation:

If something is decreasing by 7% we can mulitply it by (1-.07) or .93

so our formula is

100(.93)²⁰= 23.42388737

which rounds to 23.42

Using the exponential decline function ; the cost of the item after 20 years would be $23.42

Recall :

Substitute the values into the equation :

[tex] y = 100(1 - 0.07)^{20} [/tex]

[tex] y = 100(0.93)^{20} [/tex]

[tex] y = 100(0.23423887366)[/tex]

y = $23.42

Therefore, the cost of the item after 20 years is $23.42

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Answer:

10 units

Step-by-step explanation:

Given that,

The area is modeled by the equation as follows :

[tex]A=-l^2-10l+300[/tex]

Where

l is the linear dimensions of the frame.

Put A = 100

So,

[tex]-l^2-10l+300=100\\\\-l^2-10l+200=0\\\\l=10,-20[/tex]

So, the linear dimension of the frame is equal to 10 units.

Answer:

1) x = -17 +6y + 2z/3

2) x= -13 - 4y - 5z/6

3) x= -22 +4y + 3z/3

Step-by-step explanation:

1) 3x-6y-2z=-17

3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )

3x=-17+6y+2z

3x/3= -17/3 +6y/3 + 2z/3

x = -17 +6y + 2z/3

2) −6x+4y+5z=13

-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )

-6x=13-4y-5z

-6x/-6= 13/-6 - 4y/-6 - 5z/-6

x= -13 - 4y - 5z/6

3) −3x−4y−3z=22

-3x=22+4y+3z

-3x/-3 = 22/-3 + 4y/-3 +3z/-3

x= -22 +4y + 3z/3

Answer: 1.25 square feet

This converts to the improper fraction 5/4

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Explanation:

The area of the triangle on the left is base*height/2 = 0.5*2/2 = 0.5 square feet. Note that 1/2 = 0.5

The area of the triangle on the right side is base*height/2 = 0.2*3/2 = 0.75 square feet. This converts to the fraction 3/4

Add up the two results: 0.5+0.75 = 1.25 square feet

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If you need the answer as an improper fraction, then,

1.25 = 1 + 0.25

1.25 = 1 + 1/4

1.25 = 4/4 + 1/4

1.25 = (4+1)/4

1.25 = 5/4

Answer:

[tex]1\frac{9}{12}[/tex]

Step-by-step explanation:

Convert any whole numbers to improper fractions

[tex]\frac{9}{4}-\frac{3}{6}[/tex]

Find the LCM of the denominators and use multiplication to change the denominators to the LCM

[tex]\frac{27}{12}-\frac{6}{12}[/tex]

Subtract

[tex]\frac{21}{12}[/tex]

Simplify

[tex]1\frac{3}{4}[/tex]

[tex]1\frac{9}{12}[/tex] can be simplified to [tex]1\frac{3}{4}[/tex] so the answer is [tex]1\frac{9}{12}[/tex]

Answer:

0.3 probability that [tex]x \leq -3[/tex]

Step-by-step explanation:

The probability distribution is given in the table.

Probability that x <= -3

The values that are -3 or lower are -3 and -5. So

[tex]P(X \leq -3) = P(X = -3) + P(X = -5)[/tex]

From the table:

[tex]P(X = -3) = 0.13, P(X = -5) = 0.17[/tex]. So

[tex]P(X \leq -3) = P(X = -3) + P(X = -5) = 0.13 + 0.17 = 0.3[/tex]

0.3 probability that [tex]x \leq -3[/tex]

Answer:0.3

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

numbers taken = 1 to 40

multiples of 2 are = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40}

so there are 20 favourable  outcomes.

probability = 20/40

=1/2

for multiples of 3

multiples = {3,6,9,12,15,18,21,24,27,30,33,36,39}

there are 13 favourable outcomes

probability = 13/40

since there is no 13/40 the answer should be the probability of multiples of 2 i.e 1/2

Answer:

ABC is congruent to EDC because m<3 = m<4 and m<1 = m<5

Step-by-step explanation:

m<3 and m<4 are vertical angles so they are congruent. m<1 and m<5 are alternate interior angles so they are also congruent.

Answer:

I think the answer is the sequence is arithmetic because the term have a common difference

The correct option is The sequence is not arithmetic because the terms do not have a common difference.

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k called the common difference.

Given is graph, we need to conclude the true about the graph,

Finding the common difference,

4-1 = 3    

9-4 = 5

16-9 = 7

25-16 = 9

Clearly from the set of values that are given in the graph we could observe that the function that is formed using these set of values is:

y=f(n)=n² where n=1,2,3,4,5,.....

That mean, the following sequence is not an arithmetic sequence as the common difference is different.

Hence, the correct option is The sequence is not arithmetic because the terms do not have a common difference.

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Answer:

B

Step-by-step explanation:

SOH CAH TOA

sin theta = opp/hyp

csc theta = hyp/opp

csc theta = 10/8 = 5/4

cos theta = adj/hyp

sec theta = hyp/adj

sec theta = 10/6 = 5/3

Answer: B

Answer:

[tex]h(x) = \sqrt{x+5}[/tex], option C.

Step-by-step explanation:

The parent function is [tex]f(x) = \sqrt{x}[/tex]

Function h:

Function h is function f shifted left 5 units.

Shifting a function f a units to the left is the same as finding [tex]f(x+a)[/tex]

Thus:

[tex]h(x) = f(x+5) = \sqrt{x+5}[/tex]

The function is [tex]h(x) = \sqrt{x+5}[/tex], and thus, the correct answer is given by option C.

Answer:

          c        

Step-by-step explanation:

Answer:

El p-value de lo teste es de 0.0475 > 0.01, o que implica que con base en estos datos, no es posible concluir que el IQ medio para la población es menor de 100.

Step-by-step explanation:

Teste que IQ medio para la población es menor de 100

En la hipótese nula, lo teste es se el IQ medio eres de al menos 100, o sea:

[tex]H_0: \mu \geq 100[/tex]

En la hipótese alternative, lo teste es se el IQ medio es menor de 100, o sea:

[tex]H_1: \mu < 100[/tex]

La estatistica de teste es:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

En que X es el promedio de la muestra, [tex]\mu[/tex] es lo valor testado en la hipótese nula, [tex]\sigma[/tex] es la desviacion estandar y n es lo tamaño de la muestra.

100 testado en la hipótese nula:

Entonces [tex]\mu = 100[/tex]

Desviácion esstándar de 15: Una muestra aleatoria de 25 adultos procedentes de esa población tiene un IQ medio de 105.

Esto significa que [tex]\sigma = 15, n = 25, X = 105[/tex]

Estatisitica de teste:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{105 - 100}{\frac{15}{\sqrt{25}}}[/tex]

[tex]z = 1.67[/tex]

P-value de lo teste e decisión:

El p-value de lo teste es la probabilidad de encontrar una amostra com média abajo de 105, que es 1 subtraído por el p-value de z = 1.67.

En la tabla-z, z = 1.67 tiene un p-value de 0.9525.

1 - 0.9525 = 0.0475

El p-value de lo teste es de 0.0475 > 0.01, o que implica que con base en estos datos, no es posible concluir que el IQ medio para la población es menor de 100.

Answer:

maybe u missplaced it somehow and it also would depend if you trust that person or not. some times that 'friend' can turn out to be fake but i don't mean it about ur friend. for now, u should just ask, there's no harm in that.

Answer:

B,C,D

Step-by-step explanation:

Square both sides of the equation to get rid of the square root surrounding x.

sqrtX^2 = x and 7^2 = 7*7 = 49

x<49

And since we have a radical, we have to have non-negative solutions (the radical used in the equation actually only means the positive square root) meaning x>0

So which one of the choices is less than 49 and greater than 0?

B,C, and D are all less than 49, and greater than 0

Answer:

I thimk it is B

Step-by-step explanation:

Answer:

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Step-by-step explanation:

Given

[tex]Pennies = 22[/tex]

[tex]Dimes = 27[/tex]

[tex]Nickels = 9[/tex]

[tex]Quarters = 30[/tex]

Required

[tex]P(Penny\ and\ Dime)[/tex]

This is calculated as:

[tex]P(Penny\ and\ Dime) = P(Penny) * P(Dime)[/tex]

Since it is a selection without replacement, the computation is:

[tex]P(Penny\ and\ Dime) = \frac{Penny}{Total} * \frac{Dime}{Total-1}[/tex]

So, we have:

[tex]P(Penny\ and\ Dime) = \frac{22}{22+27+9+30} * \frac{Dime}{22+27+9+30-1}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{22}{88} * \frac{27}{87}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{1}{4} * \frac{9}{29}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Answer:

Hence the correct option is option d.

Explanation:

We can 95% confident that between 28.1% and 39.2% of all rental property owners own a property by the water.  

Here correct option for interpretation of the 95% confidence interval. The remaining options are about probabilities and sample proportions.

Answer:

Step-by-step explanation:

y = mx + b is the slope-intercept form of a line where m is the number value of the slope and b is the number value of the y-intercept. Our slope is given as 7, therefore, m = 7 in our equation. Our y-intercept is given as -10; thus, b = -10. Filling that in gives us y = 7x - 10

Answer:

BC = 4 units

Value fo y = 44

∠DAB = 56°

Value of x = 2

Step-by-step explanation:

100 - y = 12 + y  (opposite angles of parallelogram are equal)

2y = 88

y = 44

Similarly,

6-x = x+2   (opposite sides of parallelogram are equal)

2x = 4

x = 2

Answer:

The limit is 0, and the answer is given by option E.

Step-by-step explanation:

Limit to the right:

The limit of a function approacing a value of x to the right is given by the value of the function quite close to the point, looking to the right.

In this question:

Approacing by the right(x quite close, but more than -1, that is, -0.9999...), y tends to 0, so the limit is 0, and the answer is given by option E.

Answer:

decrease by 5

Step-by-step explanation:

n= 10

then in sequence,

n= n-5

Answer:

1660

Step-by-step explanation: