If the area of a triangle is 36 in.^2in. ​2 ​​ and the base is 9 in., what is the height of the triangle?

Answer:

Graph A

Step-by-step explanation:

The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.

I hope this helps :))

The graph A is correct.

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

The equation is,

[tex]y=2(0.5)^{x}[/tex]

Plotting the graph, we get,

Option A

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Answer:

B, E

Step-by-step explanation:

A line has a negative slope when it decreases going left to right.

As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).

Answer:

B & E

Step-by-step explanation:

The probability that all 4 selected workers will be from the day shift is, = 0.0198

The probability that all 4  selected workers will be from the same shift is = 0.0278

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257

To solve this question properly, we will need to make use of the concept of combination along with set theory.

In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.  

The formula for calculating combination can be expressed as:

[tex]\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}[/tex]

From the parameters given:

A quality control consultant is to select 4 of these workers for in-depth interviews:

Using the expression for calculating combination:

(a)

The number of selections results in all 4 workers coming from the day shift is :

[tex]\mathbf{(^n _r) = (^{10} _4)}[/tex]

[tex]\mathbf{=\dfrac{(10!)}{4!(10-4)!}}[/tex]

= 210

The probability that all 5 selected workers will be from the day shift is,

[tex]\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}[/tex]

[tex]\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}[/tex]

(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:

P( all 4 selected workers will be) [tex]\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}[/tex]

where;

[tex]\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}[/tex]

[tex]\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}[/tex]

P( all 4 selected workers is:)

[tex]\mathbf{=\dfrac{210+70+15}{10626}}[/tex]

The probability that all 4 selected workers will be from the same shift is = 0.0278

(c)

The probability that at least two different shifts will be represented among the selected workers can be computed as:

 [tex]= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}[/tex]

[tex]=1 - \dfrac{210+70+15}{10626}[/tex]

= 1 - 0.0278

=  0.9722

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

(d)

The probability that at least one of the shifts will be unrepresented in the sample of workers is:

[tex]P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]

[tex]P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]

[tex]P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0[/tex]

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257

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Answer:

Step-by-step explanation:

A= New amount

P= Principal or Original amount which is £1500

I= Interest

t= time period

3.5% as a decimal is 3.5÷100=0.035

time period= 4 years

so 1500(1+0.035)^4 = B

Answer:509

Step-by-step explanation:600

Answer:

(A) [tex]y=-0.762+0.119x[/tex]

(B) If a country increases its life expectancy, the happiness index will increase.

(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Step-by-step explanation:

A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).

The output of the regression analysis are as follows:

a = -0.762

b = 0.119

r² = 0.8649

r = 0.93

(A)

The equation of the Least Squares Regression line of the form y = _ + _ x is:

[tex]y=-0.762+0.119x[/tex]

(B)

The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.

The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.

Thus, if a country increases its life expectancy, the happiness index will increase.

(C)

Compute the value of y for x = x + 3.5 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]

Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D)

Compute the value of y for x = 67 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]

Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Answer:

14

Step-by-step explanation:

each square is 2 you count across then up or the other way is fine too from point A to B it equals to 14

Answer:

it's b 59° because it's at the side

Answer:

the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.

Step-by-step explanation:

With the statement we can make a system of 2x2 equations, where:

"x" is the area of the first field

"y" is the area of the second field

However,

x + y = 56 => x = 56 - y

3/4 * x + 2/3 * y = 40

replacing we have:

3/4 * (56 - y) + 2/3 * y = 40

42 - 3/4 * y + 2/3 * y = 40

-0.0833 * y = 40 - 42

y = -2 / -0.0833

y = 24

now for x:

 x = 56 - 24

x = 32

This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.

I'm assuming the limit is supposed to be

[tex]\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}[/tex]

Multiply the numerator by its conjugate, and do the same with the denominator:

[tex]\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)[/tex]

so that in the limit, we have

[tex]\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

Factorize the first term in the denominator as

[tex]x^2-3x=x(x-3)[/tex]

The [tex]x-3[/tex] terms cancel, leaving you with

[tex]\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

and the limand is continuous at [tex]x=3[/tex], so we can substitute it to find the limit has a value of -1/18.

Answer:

0

Step-by-step explanation:

6-24n=3n+6

Add 24n to both sides of the equation:

6=27n+6

Subtract 6 from both sides:

27n=0

Therefore, n=0.

Hope this helps!

Answer:

The answer is s / s + 3

Step-by-step explanation:

I applied the fraction rule a/b divided by c/d = a/b times c/d

Please mark BRAINLIEST!

Answer:

B

Step-by-step explanation:

In that scenario, you would have one T and two H's, in any order. Looking at the chart, this happens in 3 different scenarios. Since there are a total of 8 possible outcomes, the probability of this happening is 3/8 or answer choice B. Hope this helps!

Answer:B

Step-by-step explanation: the number of event is 3 event={HHT, HTH,THH }

And the number of sample space is 8

By using 2^n formula our n is 3 2^3 = 8

The probability = 3/8

Hope it helps

Brainliest please

Answer:

El resto es 9.

Step-by-step explanation:

En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.

Answer:

(1)  f(x,y) = 1-|x|-|y|

(a) 3d figure attached

(b) 2d figure attached

(2) f(x,y) = 6-2x-3y

(a) 3d figure attached

(b) 2d figure attached

Step-by-step explanation:

The Function is not given in the question. Lets solve this for 2 common function for the internet. Hopefully it can solves the given problem

(1)  f(x,y) = 1-|x|-|y|

(2) f(x,y) = 6-2x-3y

All the figures are labelled to avoid confusion. (a) part of both functions have 3D sketches. (b) part of both functions have 2d sketches

Answer:

43

Step-by-step explanation:

If X + 21 = 64

then subtract 64 by 21 and you get 43

Answer:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]

So the answer for this case would be n=369 rounded up to the nearest integer

Step-by-step explanation:

We know the following info given:

[tex] \sigma = 1.8[/tex] represent the standard deviation

[tex]\mu = 5.8[/tex] the true mean that she believes

[tex] ME = 0.12[/tex] represent the margin of error

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]

So the answer for this case would be n=369 rounded up to the nearest integer

Answer:

8 units.

Step-by-step explanation:

The smaller of the right triangles formed is similar to the whole triangle so

4/x = x/16   where  x = the shorter leg

x^2 = 64

x = 8.

The length of the shorter leg of the right triangle is 3 units.

Let's denote the length of the shorter leg of the right triangle as "x." Since the altitude drawn to the hypotenuse divides it into segments of lengths 4 and 12, we can set up a proportion between the two triangles formed.

According to the similarity of triangles, the length of the shorter leg to the length of the segment of the hypotenuse it divides is the same as the length of the longer leg to the length of the other segment of the hypotenuse.

So, we can set up the proportion:

x / 4 = 12 / (hypotenuse length).

Now, we know that the hypotenuse length is equal to the sum of the two segments (4 + 12 = 16). We can substitute it into the proportion:

x / 4 = 12 / 16.

Now, cross-multiply and solve for x:

16x = 4 * 12,

16x = 48,

x = 48 / 16,

x = 3.

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Answer:

2.5 sec

Step-by-step explanation:

Height of wall = 2.5 m

initial speed of ball = 14 m/s

height from which ball is kicked = 0.4 m

we calculate the speed of the ball at the height that matches the wall first

height that matches wall = 2.5 - 0.4 = 2.1 m

using  =  + 2as

where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)

=  + 2(-9.81 x 2.1)

= 196 - 41.202

= 154.8

v =  = 12.44 m/s

this is the velocity of the ball at exactly the point where the wall ends.

At the maximum height, the speed of the ball becomes zero

therefore,

u = 12.44 m/s

v = 0 m/s

a = -9.81 m/s^2

t = ?

using V = U + at

0 = 12.44 - 9.81t

-12.44 = -9.81

t = -12.44/-9.81

t = 1.27 s

the maximum height the ball reaches will be gotten with

=  + 2as

a = -9.81 m/s^2

0 =  + 2(-9.81s)

0 = 196 - 19.62s

s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.

height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m

we calculate for the time taken for the ball to travel down this height

a = 9.81 m/s^2 (positive in downwards movement)

u = 0

s = 7.49 m

using s = ut + a

7.49 = (0 x t) +  (9.81 x  )

7.49 = 0 + 4.9

 = 7.49/4.9 = 1.53

t =  = 1.23 sec

Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec

Answer:

21-25 = 4

26-30 = 3

Step-by-step explanation:

16-20 (4)= 17 17 17 18

21-25 (4)= 21 22 24 25

26-30 (3)= 26 27

30

31-35 (3)= 32 35 35

36-40 (5)= 36 37 37 38 39

41-45 (2)= 41 42

Answer:

d = 2[tex]\sqrt{17}[/tex]

Step-by-step explanation:

P1 (-5, 4) P2 (-3, -4)

Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

Plug in the values and simplify

d = [tex]\sqrt{(-3 + 5)^{2} + (-4 -4)^{2} }[/tex]

d = [tex]\sqrt{(2)^{2} + (-8)^{2} }[/tex]

d = [tex]\sqrt{4 + 64 }[/tex]

d = [tex]\sqrt{68}[/tex]

d = 2[tex]\sqrt{17}[/tex]

I hope this helps :)

Answer:

2/33

Step-by-step explanation:

Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)

Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)

8/22 = 4/11

Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11

= 4/66

= 2/33

Answer:

See below

Step-by-step explanation:

a.

[tex]\dfrac{10}{4}=\dfrac{5(2)}{2(2)}=\dfrac{5}{2}[/tex]

b.

[tex]\dfrac{20}{15}=\dfrac{4(5)}{3(5)}=\dfrac{4}{3}[/tex]

c.

[tex]\dfrac{-24}{42}=\dfrac{-4(6)}{7(6)}=\dfrac{-4}{7}[/tex]

d.

[tex]\dfrac{-18}{-14}=\dfrac{-2(9)}{-2(7)}=\dfrac{9}{7}[/tex]

Hope this helps!

Answer:

sorry'but I don't know the answer

Answer: 0.401294

Step-by-step explanation:

z=x-μ/σ

z=20-22/8

z=-0.25

the probability for this z-score is 0.401294.

Answer:

a. [tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c.  the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e.  86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability  density function can now be determined as :

[tex]f_X(x) = \dfrac{1}{B-A}A<x<B[/tex]

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x) = \dfrac{1}{12-8.5}8.5<x<12[/tex]

[tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

[tex]F(x) = \dfrac{x-A}{B-A}[/tex]

[tex]F(10) = \dfrac{10-8.5}{12-8.5}[/tex]

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

[tex]P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (12-11)[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (1)[/tex]

[tex]P(X\geq11) = 0.2857[/tex]

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

[tex]P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.2857* (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.5714[/tex]

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

[tex]P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(3)[/tex]

[tex]P(X \geq 9) = 0.2857*}(3)[/tex]

[tex]P(X \geq 9) = 0.8571[/tex]

NOW; The Number of iPad  that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

Answer:

34°

Step-by-step explanation:

According to the theorem, "any two angles in the same segmant are congruent"

<BED = <BCD

So

<BED = 34°

Answer:

P(120< x < 210) =  0.8664

Step-by-step explanation:

given data

time length = 20 year

average mean time μ = 165 min

standard deviation σ = 30 min

randomly selected game between = 120 and 210 minute

solution

so here probability between 120 and 210 will be

P(120< x < 210) = [tex]P(\frac{120-165}{30}< \frac{x-\mu }{\sigma } <\frac{210-165}{30})[/tex]

P(120< x < 210) = [tex]P(\frac{-45}{30}< \frac{x-\mu }{\sigma } <\frac{45}{30})[/tex]

P(120< x < 210) = P(-1.5< Z < 1.5)

P(120< x < 210) = P(Z< 1.5) - P(Z< -1.5)

now we will use here this function in excel function

=NORMSDIST(z)

=NORMSDIST(-1.5)

P(120< x < 210) = 0.9332 - 0.0668

P(120< x < 210) =  0.8664

Answer:

[tex]\boxed{ \ x = 1 \ }[/tex]

Step-by-step explanation:

hi,

-x+(-1)=3x+(-5)

<=>

-x-1=3x-5

<=>

3x+x = -1+5 = 4

<=>

4x=4

<=>

x=1

thanks

The value of x when solving the equation -x+ (-1) = 3x + (-5) is 1

Algebraic expression is a union of terms by the operations such as addition, subtraction, multiplication, division, etc

-x + (-1) = 3x + (-5)

The value of x can be found as follows:

-x + (-1) = 3x + (-5)

Let's open the parenthesis, Therefore,

-x - 1 = 3x - 5

-x - 3x = -5 + 1

-4x = -4

divide both sides by -4

-4x / -4 = -4 / -4

x = 1

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